When are we not 4bet/getting it in with AK?

Everyone seems to think that it's completely standard to just 4bet AK and get it in preflop in almost every situation. I am not so convinced.

Here's an example:

100bb stacks 6max $100nl
3 folds, Hero (BTN) Raises $3, SB 3bets to $10, 1 fold, Hero 4bets and calls 5bet shove.

Assume we both have Tagg images and SB is 3betting 6% from the SB and he is 5bet shoving JJ+, AK (3%).

Here's what my math says:
Half the time he folds to our 4bet and we win $14, the other half we get it in and we are a 40% underdog.

.50(14) + .50(.60(-97) + .40(104)) = -$1.30

So this is a losing play? Can someone check my math here because I was convinced this was a winning play.
I know for sure it becomes a winning play if the SB 5bet bluffs once in a while or gets it in lighter for value.

Back to my original question, which is basically asking when are we just calling a 3bet with AK preflop?
Is anyone always calling preflop in the above example versus a Tagg villain who isn't 3betting light?
What's the plan post-flop if we do just call preflop? Are we floating most flops in position?
What about when we are out of position?

Your example is one specific situation. If I'm 3bet by a tight player, then I often flat AK IP.

I don't think there's anything wrong with flatting AK to a 3bet, if there is no dynamic for him to stack off light (air, AQ etc). The same way as I don't think its bad to flat a high pair to someone who normally folds to 3bets, if there is no dynamic for them to continue or stack off light.

Clearly nobody is going to fold AK here to the 3bet. So you have to compare the EV of 4bet getting it in to flatting his 3bet. If you're prone to mistakes postflop in 3bet pots it might be more +EV to just 4bet get it in, if we assume folding isn't an option.

Yes it is one specific situation. However, the majority of players I face are 3betting less than 7% of the time. So when I have AK and get 3bet, I am up against someone who is not 3betting light the vast majority of the time.

I think when we are oop there is a stronger argument for 4betting and getting it in (positional advantage postflop). This is also opp specific, but against a standard TAG (as u mentioned) who 3bets me IP i'm more likely to 4bet get it in. If i raise CO and get 3b by an opp in the blinds whose 3b in the blinds is high i would mix it up between 4betting and calling. I dont think theres a default play but certainly a bunch of considerations to take with AK preflop.

Yea, if I don't think I can call off a 5 bet I don't 4bet with value hands very often. IP I tend to take flops. Most of the time they wo't giv eyou credit for AK because you don't get it in.

AK is far ahead of 6% 3betting, but not his calling range obviously.

that pretty much nails it