The second i disagree with. A fighter in game doesn't know his current class plateaus at any level. He doesn't know what extra attack is because extra attack doesn't simulate him swinging twice as fast instead it's about him being better skilled and more of his attacks in a round finding openings.
If you want to understand this, then you need to accept that the rules of the game reflect the reality of the game world. You need to reject the unnecessary abstractions, like saying that the less-skilled fighter is attacking just as quickly, even though observation shows us that there is a definite line of experience where they go from
never landing two blows in six second to
often landing two blows in six seconds. That was an abstraction which was useful in the days of minute-long rounds, but it detracts from the game as a statistical model. Think of it in terms of firing arrows, if it helps, since we know for a fact that each attack roll corresponds to exactly one arrow in flight.
If you accept the basic premise, that the rules of the game reflect the reality of the game world, then it is a true fact of their reality that competent warriors can fire arrows twice as quickly as less-skilled warriors, and even more-skilled warriors can fire three or (theoretically) four times as quickly. (It's also true that sometimes, very briefly, trained warriors can act even more quickly than they typically do; but it's not something anyone can keep up for very long, so they need to rest before they can do it again.) We
know that this is true, because any test that we run can
confirm it; if you put a reasonably-experienced archer against a novice, in a contest of hitting twenty bullseyes or killing twenty kobolds, the experienced archer will reach their goal in about half the time. And given that it is
empirically true that their world works that way, then it stands to reason that the characters would
know this; after all, they actually
live in that world, and we only
visit there for a couple of hours per week.
If you instead
reject the premise, and say that the rules of the game
don't reflect the reality of the game world, then you need to come up with some explanation for why every test we conduct conforms to the rules but
not to the reality. In fact, if the rules don't reflect the reality, then we have no clue to what that reality even
is. If we
don't say that one attack roll corresponds to one meaningful swing of the sword, and that a successful hit for damage means you actually
hit and
caused damage (because you want to use super-abstract HP for some reason), then we have
no idea how many swings you actually made or whether you actually hit or caused damage.
Which goes to the underlying point: If the mechanics of the game don't tell us what's
actually happening within the game world, then what good are they to us? If the DM has to make something up anyway, because the rules don't tell us what happens, then why do we need rules at all? Why does it matter what you decide to do, from an RP perspective, if none of your choices correspond to the reality that your character observes? If we want our choices to matter, and for them to be the
same choices that our characters face - if we want to actually
role-play at all - then we need the rules to reflect the reality.