lol I was just discussing this last night. I said that I thought people stacked AK too much in 6max and that in most cases flatting the 3-bet was far superior to 4-betting and getting it in. I said that against someone with a lot of history or a bvb or button vs. blind where your opponent makes a ton of moves that I still 4-bet AK for value, but that if he just 3-bets a normal ammount I would flat especially if I'm in position. Reasoning is that against 99% of the people (at least that I've played with, no idea how it is at 400nl+ 6max), if your all-in is called you are NEVER ahead. No one calls preflop shoves with AQ at least at 200nl. Basically your shove folds out hands you beat and gets calls from hands that beat you and some that flip (AK/QQ/maybe JJ). Meanwhile if you flat, if you hit an A you could stack AQ/AJ or if not stack extract a lot more money postflop. Stacking a K will make a good amount more off KQ if not a stack. The point is these are the hands that put in 0 more money preflop but certain opponents may stack off with it because they hit top pair in a 3-bet pot.
That said I'm absolutely shocked at your graph. Although I think flatting is superior in many cases, I really can't believe it's costing you an average of 15 big blinds per shove. Although honestly I'd like to see it filtered to pots where there is a 4-bet or all-in. Say you raise, get 3-bet, 4-bet to w/e you 4-bet to (I'm not thinking you 4-bet shove a ton) and they fold. You're getting like 10-14 big blinds right there depending on your raise size and their 3-bet size meanwhile there's never an all-in. The 4-bet is what prices you in too. If you 4-bet to like 30 big blinds, AK still has odds
to call a shove from a range of KK+/AK. But when stacks do go in you only have 38% equity.
So I think that's most likely the problem, check out 4-bet pots because by that time you're mostly committed and since your opponent knows that you should get a lot of folds from 4-bets that will probably make AK positive for you, but as I said in certain situations I believe flatting AK to 3-bets in position can be much more profitable than 4-betting it against most opponents in 6max. Obviously if they're 3-betting like 15% I just raise and get it in but against a standard 3-bet percentage of like 5-8% I would experiment flatting more, although I haven't played a ton of 6max in the last few months and haven't tested this theory at all so it could be completely off.