Define "choice of game".
If I have a miserable time playing D&D, I don't necessarily need to revisit my choice to play D&D. There are many possible reasons for the miserable result, only one of which is the ruleset itself. I may need to revisit how I am playing D&D - it isn't like there's only one way to play.
I'm curious as to why you didn't apply your suggestion to
@pemerton's statement but instead assumed that he must be speaking about switching systems?
Well, the
game I had in mind is the one that has the sort of structure I had pointed to in my post to which you (Umbran) replied and had described in a bit more detail not far upthread of that post. Namely, a game in which there is a "mission" that establishes a success condition, be that the sort of loot-extraction that characterises Gygax-ish D&D, the overcoming-of-the-challenges-presented that characterises (say) what seems a fairly common approach to 3E and 5e, or the resolve-the-mystery/plot/scenario presented by the GM, which has been common in D&D at least since the 2nd ed AD&D era.
This sort of game is characterised by a particular sort of prep phase for the GM participant - be that building the dungeon (maps, keys) or working out the scenario (often maps here too, as well as timelines and event sequences) or writing up the encounters (more maps, stat blocks). And by a certain sort of expectation on the players - that they will engage that prepped content in the appropriate spirit.
Now there's no stopping human creativity and genre subversion, and apparently even way back in the day there were dungeons which, when properly mapped, spelled out jokes or rude words or whatever. Maybe those dungeons had ogres in them that threatened to argue the PCs to death a la Monty Python treated as literal rather than ironic? - I don't know for sure. But at a certain point it seems to me to make sense to ask the following:
if we don't like the structure and premise of the play we're purporting to engage in, why are we still doing it?
As to whether this involves changing rulesets, that depends on what one treats as the identity conditions for a ruleset. I've recently discovered the cooperative card game The Crew. It's a whist variant: there is a deal of hands, then an auction phase (in which "tasks" ie requirements to win particular tricks) are allocated, and then a card play phase. Good play uses the standard skills of whist-like games: keeping track of which cards are played in which suits, noting and exploiting voids, etc. But unlike (say) five hundred it's fully cooperative rather than a combination of cooperation (between partners) and competition (between partnerships), and this changes the dynamic of play.
We can look at D&D through this same sort of of lens of what stays the same and what changes. If you change the XP rules for D&D, for instance, you can get a game with a rather different dynamic even if the basics of PC build are much the same. Or consider overlaying the Honour rules from the original OA, which create a new variation of something like an alignment subsystem which brings with it expectations that certain new sorts of scenes (eg duels and non-combat contest) will be part of the game, and generate new build demands (eg non-weapon proficiencies) to go with them,
In 4e D&D - to pick a version of D&D that I know well - as amplified by the DMG2 and Rules Compendium, XP are awarded for engaging in any encounter (skill challenge XP are earned whether the PCs win or lose; combat XP are earned for defeated foes whether or not the PCs win the combat overall or not), for achieving goals which the system encourages to be player-authored (Quest XP), and for otherwise spending time engaging the fiction even if the action is not being resolved via mechanics (as per the DMG2). In other words, basically any engagement with the game earns XP and hence, over time, levels. And the treasure parcel system means that any earning of levels earns treasure, with the system encouraging the GM to accommodate that treasure to player preferences (eg via "wish lists).
So in 4e D&D, we have basic elements of PC build that are recognisable even to a AD&D player (the six attributes, hit points, defence numbers, skill bonuses that resemble NWPs, lists of player abilities that resemble spells or OA ki powers, etc). But what does it mean to have my PC
act suboptimally? I know what that means in Gygaxish AD&D - because my PC is
reckless I charge down the hallway without checking for traps and get ganked by a scything blade. My PC is injured or even dead and I've earned no XP and not really progressed us towards our goal. But in 4e the significance of exactly the same series of events is completely different (eg confronting a trap is worth XP, as per the encounter rules; and hit point loss plays out with a completely different mechanical significance because of the healing rules).
In AD&D - and here the actual play experience I have in mind is my own play of OA in the mid-to-late 80s - if we change the PC build rules to include families, loyalties, aspirations for honour, etc; and the GM changes the way setting is authored and presented having an eye on these things; and we change the XP rules to reward overcoming challenges and achieving goals independent of treasure gained (which at the time I had kinda done in a piecemeal fashion following a Dragon article; and some character classes had their own rules for this, like shukenja earning XP for healing NPCs); are we still using the same ruleset? I don't have a dogmatic view on that, but it's clearly not identical. And I can report from my own case that it significantly improved the play experience.
And to finish this post: if a group wanted to keep the "mission" structure as the basic spine of their fiction; but wanted to encourage players to portray characters in a way that is somewhat orthogonal to the mission; then I would suggest looking at how XP-for-Milestones works in Marvel Heroic RP. Sticking to the "official" goals of play under those circumstances just seems a bit counterproductive.