That only makes sense if you think that the combat is all what is D&D about
It's always been a major focus of the game, sure, but the CaW/CaS metaphor sums up and makes judgement about games based only on combat. Thus 'Combat as...'
Yet this is not the case. D&D, at least theoretically, is not only about combat so "cheating" in combat, I would rather call it using strategy instead, is as part of the RPG than is duking it out honourably.
Sure, but it's more theoretical at some points in it's history than others. The game has mostly had lots of rules for combat, lots of rules for spells, and not a lot of rules for everything else - the other 'two pillars' as non-combat has recently been refined.
So when you judge a game by a metaphor on how it supposedly approaches combat - however invalid the metaphor may be - it's implicit that it's a game about combat, and that the system is dictating the approach, rather than the approach being a matter of style.
That's all wrong, of course, not just the combat-only assumption.
By trying to remove most of the strategy from the equation by making combat more like a sport the only thing the designers succeeded in was to invalidate many playstyles and to make D&D even more into a wargame
OK, one point at a time:
First of all, what
strategy did WotC start
removing from the game over it's tenure? That is, what strategy was actually there, as part of the game, before they started 'removing' it? (Yeah, that's rhetorical.)
The answer is really 'not much.' The game, itself, mechanically was a resource-management challenge centered around spells and hps, and the primary resources renewed by retiring from the dungeon to rest. The goal was exp, which got you more such power, and acquiring treasure, especially magic items, which got you more power.

Prettymuch a video game, really - successful play earning more play at a higher level. Any 'strategy' beyond the timing of resources was just an interplay between the player proposing a course of action and the DM deciding how well that worked out for him. Not game, not even meta-game - just the player persuading the DM to rule in his favor. There was a lot of room for that, but calling it 'strategy' is pushing, or at least, spinning it, rather a lot. 'Gaming the DM' would be, as or more valid, spin in the other direction.
Now, WotC did start filling in the missing pieces by having mechanics do more of the basic modeling, and by providing the DM with more guidelines. Skills, character customization options like feats, and, of course, CR, are all examples of that, giving players more control over defining their characters and making informed decisions based on what the characters were mechanically capable of, and giving DMs a (rather poor) yardstick for how challenging a given monster would be relative to the level of a 'typical' party. 4e continued that trend, 5e pulled back from it considerably - players can still customize their characters to a fair degree, but can't be confident in all of their abilities, so it's less about tactically or 'strategically' using the character's abilities, and back to being more about leveraging your relationship with the DM to get favorable rulings. Which is, of course, evocative of the classic game.
By trying to remove most of the strategy from the equation by making combat more like a sport the only thing the designers succeeded in was to invalidate many playstyles and to make D&D even more into a wargame
Now, CaW and CaS make a lot more sense as metaphors for
play style, specific to combat, than they do for games. The CaS play style is to approach a combat like a mini-game or like a scene in a story. The objective is to have a fun game or an entertaining scene - that scene plays out, and the fun happens, in the combat, itself. It's, obviously, a perfectly reasonable way to approach playing an actual game.
The CaW play style is to approach combat like an obstacle, and overcome it with a minimum of risk and resource expenditure. The objective is to trivialize the combat, ideally, to remove it as an obstacle with no risk and no resources expended. That may not seem like a lot of fun or excitement, but it's its own form of fun and some folks really like it - and it's still a game, in spite of the 'War' metaphor. The fun just doesn't happen in the combat, itself, which should be one-sided & play out quickly or even be narrated by the DM without touching dice, as the perfect plan unfolds, perfectly, but in the /preparation for the combat/.
Where CaW/CaS falls down is when it's used as a metaphor for the game, instead of the style. A game that lacks a statistic like CR is less convenient to use in a CaS mode, but that doesn't mean it can't be used that way, nor that it 'supports' CaW. It just lacks something. A game that has a CR statistic may be more convenient to use for CaS, but it's not any less convenient to use for CaW, in fact, it's still a useful tool to the DM running for players in the CaW style, just a less important one.
So, when 3.x introduced CR, it didn't
'invalidate a style,' it merely became less inconvenient to use in an additional style, it expanded support to more styles. If people gravitated towards the newly-enabled style, it could only be because they found that style, now that it was no longer as impeded by as severe a lack of tools, desirable on some level.
Really, the shift from what the community now calls DM Empowerment to Player Entitlement and back again over WotC's custodianship of D&D is more significant than the CaW/CaS (as metaphors for play style) shift, which was really only from supporting neither (but favoring CaW, because it thrives on ill-defined parameters, dysfunctional rules, and gaming the DM), to supporting both, to supporting CaS less well.
DM Empowerment favors CaW gaming-the-DM strategies, of course, but that's just one minor aspect of it, arguably not even a benefit (arguably a disadvantage).
The benefits of DM Empowerment are really something.
By trying to remove most of the strategy from the equation by making combat more like a sport the only thing the designers succeeded in was to invalidate many playstyles and to make D&D even more into a wargame
D&D started as a
wargame, and founded RPGs more or less by accident. It'll always have those wargaming roots, and acknowledging them, and enabling play in such a style (there's playstyles again) is in no way a bad thing.
(as they enforced the view that the combat is the only important part which should not be "cheated" at with whatever you do outside combat)
Not so much, no. D&D did briefly flirt with what indie RPGs call 'scene framing,' and the like. Getting to 'the action' or defining the challenge, and concentrating on that, rather than on setting it up. What that action is, though, can be a matter of style.
Let's look at a stereotypical D&D adventure. A nasty band of monsters is holed up somewhere, raiding a town. A nasty band of adventurers is recruited from the tavern to get rid of the monsters.
In the CaW style, the players investigate the town, the aftermath of the attacks, question townspeople to determine the nature & number of the monsters, make preparations, scout around, find tracks or other evidence, trace it to the monsters lair, retreat, make more preparations, observe the lair, take an isolated prisoner and torture & question it, repeat the process to confirm it's information, make more preparations, enter the lair in extreme stealth mode (quite probably only one actual PC doing so), gather first-hand reconnaissance, withdraw, prepare, strategize, prepare, and come up with a plan of attack (or attacks), run it by the DM, perform more planning/recon/preparation, reach a consensus among the players & DM on an assault that will work, and execute it. That could be multiple sessions, with only the first part of the last session being the execution (and the rest being securing the site, stripping it of all valuables, divvying them up, collecting from the town, recovering resources, gaining levels, &c).
In the CaS style, the players & DM reach a consensus about the parameters of the combat challenge, the PCs investigate the threat, locate the lair, decide whether to assault it or harass it, and do so. Play moves quickly from the intro to the first combat scene, which is played out in detail, resolved, and bridged to the next, and great fun is had by all until the last enemies are defeated. That could be multiple sessions, most of each dedicated to the 'action scenes' of the combats, the last probably almost entirely to some climactic battle, with a few minutes of bookkeeping at the end as everyone levels up.
Those are styles, but they say nothing about the game. If you wanted to play, classic D&D in either style, you could, you'd just have challenges. Very different challenges.
Taking the CaW approach means working almost entirely outside the mechanics of the system. Aside from an initial reaction roll, there's no rules covering interacting with the townspeople, the PCs don't interact with the townspeople, the players interact with the DM, pumping him for information. Similarly, aside from one ranger special ability, there's no rules for tracking the monsters back to their lair - though a spell might just reveal that location. So, the players interact with the DM, the DM describes the area, the players describe investigating it, the DM coughs up clues until the players figure it out. Similarly on down the line, the rules provide little coverage for the players' activities, and, where they do, they're often unfavorable, so it behooves them to keep the action to levels where the DM decides what happens based on what they're doing, not what they're characters are capable of.
Conversely, taking the CaS approach is a challenge for the DM. The players want to just 'get to the fight,' so the DM prepares a fight, he has no guidance, maybe he uses too few monsters, and the fight is a quickie let-down, maybe too many or too strong and it goes badly, someone's knocked to negatives and they spend a week in town, or someone's playing a new character next session, or the DM shifts gears and starts soft-balling a combat so the players can make it through and it becomes a comical slog of fudged misses and implausibly low damage rolls behind the screen.
CaW was largely unsupported by the classic game, but, if the DM let it, it could work out quite satisfactorily. CaS was largely unsupported by the classic game, and until the DM was a past-master of the art of DMing, it would often go very badly, indeed.
5e intentionally harkens back to that.
Contrast that with a more 'modern' (90s or current 'indie' game or peak-"CaS" WotC D&D) system. Played in the CaW style, the scenes are framed as intro/exposition (interacting with townspeople), mystery (what are the raiders, where are they hiding?), foreshadowing (scouting, taking a prisoner, etc), grand strategy (planning and preparing for the raid), and denouement (the raid & it's aftermath). Each scene is played through in detail, using the resolution systems best suited to it. The combats implicit in the raid may be mostly narrated, or highlights of each played through quickly as part of a broader resolution, perhaps as consequences of partial failures along the way.
Played in the CaS style the scenes are framed as a series of exciting/challenging battles. That framing includes learning about the raiders from the townsfolk, investigating the evidence they left behind and looking for their lair - all to set up a battle with a patrol. Questioning that prisoner is part of the framing for the next scene - the first battle in the lair, itself. From there it's a series of fights in the lair, book-ended by a little bookkeeping and scene-framing. The system provides detailed/engaging resolution with plenty of meaningful player choices for the combats, just as it does for any other scenes.
That's what I mean about the typical CaW/CaS rant being a way of acknowledging a better game while talking it down. Yeah, relative to the poor support for CaS in the classic game likely giving bad results, the poor support for CaW leaving players room to finagle favorable results could be taken as encouraging/supporting/validating that style over the other - while solid support for both, can, relatively speaking, be taken as 'discouraging' CaW.
Then again, there's no reason to focus only on challenging combat, nor exclusively on trivializing combat: an equally valid (set of) playstyle(s) would be to engage in both the more interesting non-combat scenes (whether they might influence later combat difficulties or not) and the more dramatic combat scenes. Another problem with CaW/CaS, it presents two rather extreme playstyles as a dichotomy.