"Why it's correct to play AK like this OOP against unknown?"
Well, preflop is an easy 3bet for value, u put money in the pot with a hand that dominates his calling range and plays quite well postflop, u dont need any explaining there do you.
This is a good flop to cbet, since its semi-dry (so u have very decent fold equity) + u have two overs when called, so a lot of good turn cards (either those who improve your hand or those you can barrel profitably).
Once you get called, that turn card only improves his perceived range, so hes not folding much that he called the flop with + our equity dropped significally, so its an easy c/f (at these limits especially).
Now, i dont know why you think that this line isnt profitable, you made the most ev+ decision on every street. Maybe its because you arent barreling enough good turn cards, so you feel like you always lose when you dont hit a pair. In that case, you should work on recognizing which spots are good for a double barrel and which arent and then you shouldnt have any dilemma why it is profitable to play AK oop this way.
Just think about it:
1) opponent folds pre
2) you hit a pair or better and get a lot of value from his dominated hands, since the pot is already quite big
3) you cbet w/o a pair and he folds
4) you cbet w/o a pair and he calls and you spike on the turn
5) you cbet w/o a pair and he calls and you barrel a good turn card and he folds
So many ways to win and so much value in playing AK like this, its ridicilous.