Mathematically vs that range yes. What i shouldve said was we dont know that he gets in that range preflop. He might be only all in pre with KK+, we dont know. So when i 4b there and get shoved on, i want to fold unless i have proof that he can have AK in that spot.
We're in a BTN vs BB spot. 3bet stacking AK is the most standard thing in the world. {AK, QQ+} really is the strongest range we could ever come up against.
We are much more likely to see this range widen than see it shrink.
4betting QQ here is the preflop equivalent to raising up straight flush draws. We get fold
equity and on average our equity is 40% at worst vs villains range. It will never be -EV (unless you 4bet/fold) but arguments can be made based on the players 3bet/5bet ranges whether flatting will make us even more money.
If villains 5bet range is only {AK,QQ+} we should 4bet
bluff them to death. Eventually we will have built up enough history that 4betting QQ and even 99-JJ based on the rate villain adjusts at will become the best plays.