But don't we lose value of our hand??? We want to put more chips in being in the hot seat... with a premium hand, because flatting we are letting trashy hands come out and there won't be too many good boards for us if we miss.
Plus we lose Fold equity...
What if we Flat and the board goes JT2 and our opponent leads out for a pot size bet? He prolly would've checked to us if we had 3betted and we'd have control of the hand?...
Also if we just flat we are giving our opponent information that we don't have AA KK QQ... So a lot of boards we can't represent it and we are turning into a bluff and it'll look obvious as well.
175bbs deep hands have very little preflop intrinsic value. We need a lot more information before we find out how much we want to commit to this pot. It's very easy to overplay AK preflop with deep stacks, but it is not necessary.
By flatting you keep his whole range on the hook while playing an underrepresented hand in position. When you 4bet you're folding out his AJ KQ type hands and leaving yourself facing a stronger range when he calls.
There's a lot of different ways to play AK when you are deep stacked. Arguments can be made for and against all lines.
I recommend to flat the 3bet because I'll be in position in a heads up pot and I'm confident in my post flop skills. And I don't have to hit the flop to win the pot.
But if he leads out pot sized on a JT2 board then I just fold. Easy. We don't have to win every pot we play and we don't have to push every small edge (real or imagined) to the limit.
If the OP had flatted and the flop came JT2 he might have won a smallish pot with a simple Cbet instead of losing most his stack in an unnecessary flip.