I've been enjoying this thread, even if some of the posts border on getting a bit personal at times. I find my personal position is similar to
@iserith . As a new DM (I DM'd in the 80s but didn't run TTRPGs again until 5e came out), I found the CR rules in the DMG to be useful to give a rough ball park estimate of encounter difficulty, but then quickly realized that with my players, who are very tactical and veteran players, that I would need to make an encounter at least deadly and usually rachet it it up as if for higher-level characters to make it sufficiently challenging.
At the same time, I agree with
@EzekielRaiden in that the results can be very wonky. At higher levels, and with more experience under my belt, I just don't bother calculating CR. I design encounters based on what I know about my players and, well to be honest, on personal intuition.
I never played 4e, but a friend of mine who is a hard-core gamer that has played every edition since the 80s sung the praises of 4e's encounter building rules. It is just one source anecdotal evidence, but I trust his opinion on these things.
My question for those who have given this a lot more thought than I have is: "what is the fix?" CAN you create a better CR system that doesn't require completely overhauling the entire system?
I don't know if it's a fix, but the way I'd do it is much how 3e did it. They cited their expectations. They said "we built the CR system based on four characters using the default array, who are playing a Fighter, Rogue, Cleric, and Wizard using the PHB rules, with wealth by level adhered to." All stop.
Now granted, even some PHB content could "rock the boat", as it were; magic item creation (even without entering the quagmire of custom item creation), Leadership, faulty assumptions about what spells players would use, and old busted spells that were put into the book because "the fans expected them".*
But by and large, if your 3e game ran into trouble, you could easily point to one of the above assumptions having been broken in some way (I'm not discounting player skill having an effect on the game, of course, but altering the base assumptions was something that happened way more often in my experience. Every group I ever played with had mixed tiers of player skill, but YMMV).
Now, what are 5e's assumptions? It can't be point-buy, because that's an "optional" method of creating characters (says so right in the PHB). No Feats (optional). No Magic Items (optional). Character classes? Uh, well, they keep telling us "play what you want", which rings about as true as when Blizzard told us "bring the player, not the class" in World of Warcraft raiding.
What the "baseline" is in 5e is murky, and it's violated by WotC in their own adventures! Just look at how many magic items are in them (heck, just look at Lost Mines of Phandelver!).
Now, having said all of that, I don't think just tossing out the encounter creation rules is a good idea. The fact that we don't understand WotC's monster creation rules fully (beyond that they balance for hit points vs. damage and don't really care about accuracy vs. defenses), because again, unlike 3e, where they literally said "this is how you should make/upgrade a monster", WotC just throws stuff out there without any real explanation of why a CR 5 has 15 Hit Dice, doesn't mean that we can say we know how to balance an encounter better than they can.
We can know our players and their characters, yes. But the problem I see with just deciding that CR and encounter building should be chucked out the window is that, if we reject these tools, that the game is supposedly balanced around, then we've also rejected that the game has any balance whatsoever. That each individual group of characters has to be judged on it's own merits, and it's impossible to run the game properly without years of experience as a DM.
To me, that would be a fail state for 5e as a game. So even knowing that the CR system has it's warts, I still use it as best I can. My players deserve to be treated fairly, and I can't in good conscience tell them an encounter is fair if I just tossed out enemies I assumed they could defeat, based on nothing more than "I guess"?
*(warning: tangent) I hate that WotC made this mistake not once, but twice. When they made 3e, they assumed players would be annoyed if classic spells weren't in the PHB. When those spells proved to be some of the most broken in the game, even by the end of it's production run, they removed them or altered them greatly for 4e. Which led to "this doesn't feel like D&D" backlash from people who, in my opinion, didn't really grasp why this was a good thing. And then for 5e, they brought almost everything back, and now a whole new generation of gamers is wondering wth is up with things like forcecage, simulacrum, gate, etc.. Heck, WotC even powered up some spells that didn't used to be problematic, and made them that way, like Leomund's Tiny Hut!