Not to bury the lede: Is it okay as DM to put pressure on some players to know their character enough not to slow the game unnecessarily by delaying super-rapid advancement from the party.
Absolutely. As the DM, you put more time and effort into running the game than the players do running their characters. The absolute least a player can do is be competent at the game/running their character. I would find it extremely disrespectful towards me as a person and the time and effort that i put into running the game if, after 2 YEARS!, of 'playing' that a person still didn't know how to calculate a hit bonus or figure out their damage. I would go so far as to stop inviting these people to the game.
but i can be prickly and don't tolerate people wasting my time...