What @Charlaquin said in reply to you - "what @pemerton is getting at is that playing in situations that the players are familiar with seems like a strange way to go about trying to accomplish this goal" - is right.
I can elaborate a little bit: when playing Burning Wheel, I don't have to suspend or "put on hold" any knowledge I have of the game rules, in order to play my character. (As a player. As a GM it's different, as I'll explain a bit below.) When I declare actions, knowing how the game rules for building dice pools work doesn't make it harder to play my character - it makes it easier, as I can more easily see how thinking about what my PC is trying to do (eg persuade my brother to turn away from the easy but shameful path he's taken) correlates with doing some stuff at the table (building a dice pool that has Command skill at its core). When playing out a melee combat using the full Fight! rules (which rely on a reasonably intricate structure of rock-paper-scissors-esque blind declarations), knowing how the rules work doesn't make it harder to play my character: I put my intuitions to work, script my actions, and then compare to what the GM has scripted and roll the appropriate dice.
(As a GM, when scripting combat for my NPCs or creatures I don't just rely on my intuitions. I try and also choose a sequence of actions that emulates or expresses established features of the being I'm scripting for - eg its traits and instincts. In this way, players who are aware of those trait and instincts, whether because they've already seen them manifest in play or (say) they've read them via aura-reading, can factor that knowledge into their own scripting of their blind declarations. But this is a difference between the GM and player roles: the player is advocating for their PC, whereas the GM is not advocating for the characters under their control, but rather trying to present them in a way that is true to their place in the fiction. In Apocalypse World, the analogue to this asymmetry is that the GM is bound by the principles "Make the world seem real" and "Look at your NPCs through crosshairs" but the players are not. In classic D&D the analogue is the asymmetry between the GM being bound by their notes about how NPCs will act, by reaction rolls, etc; whereas players are free to choose their PCs' behaviour as they see fit.)
I've mentioned BW, but my point generalises to most RPGs I know: being experienced makes play more smooth, and thus in some ways more satisfying, and I don't need to suppress my knowledge of how the game works in order to inhabit and portray my character.
The contrast with D&D is that, at least on a certain traditional approach, so much of D&D turns on "hidden knowledge" and related puzzles: monster immunities to damage types; the availability and properties of various spells of greater or less baroque character; the abilities of magic items; etc. When all that stuff was being invented, in the mid-to-late 70s, the knowledge was hidden not only from characters but from players, and as the players learned the knowledge they were expected to get better at the game by using it. This is why Gygax, in his DMG, suggests that new players should play the game with one another rather than with experienced players whose knowledge will dominate in play. (This is consistent with your remark about it "depending on what the players know".)
This is why my view is that, in contemporary D&D play, it makes sense to move beyond the puzzle paradigm (and so approach D&D in a fashion that is much closer to other FRPGs) or to invent new puzzles (which is what some posters in this thread say they do). You describe the latter option as "a lot of extra work" but that's exactly what the original D&D GMs were doing, as they came up with yellow mould and brown mould and shriekers and piercers and green slime and all the rest of it. On the player side, actually puzzling this stuff out was a big part of the point of play.
I'm not entirely clear, but some of what you say - eg playing my character not by asking a first person question "What should I do, given who I am?" but "What should this character do, given given the situation they are in?" - seems to expect the player to adopt the position of the GM that I've described above, no longer advocating for their character but rather (as an actor does) portraying their character according to some external criterion of adequacy. That is a very distinctive approach to RPGing, and one that to me seems at odds with the immersion in character that is (for me) the main pleasure in playing a RPG.
