People are generally way less likely to play back by 3betting a raise on the flop
See, I disagree with that. I get people shoving flops all the time with air when they're tired of me pushing them off of pots. I think the lightbulb kinda goes off in people's heads when I call them down for 2-3 streets, and they usually give up on the river. But they'll very often just jam their stack in if I make a raise.
FWIW, villain shoved in his last 3-4$ after I raised the flop. We got it all in, and he showed down
and my nines held. I'm not sure if he thought his AK was good, or was just retarded. But either way, I think we could've gotten him to shove the vast majority of his range if I raise the flop to like 12$.