I think the problem here stems from a misunderstanding of pot and ev distribution. You don't get the whole pot in the long run; you only get a fraction, except with very strong hands. Once the button limps and the small blind joins in, they have staked a claim for a fraction of the pot. While the button may have made an unprofitable play, he will still receive a fraction of the pot in the long run. Let's look at the investments:
button: 1 small bet
small blind: 1/2 small bet
big blind: zero(before raising)
after we raise AKo in the big blind and they call, these are the investments:
button: 2 small bets
small blind: 1.5 small bets
big blind: 1 small bet
the fractions of the pot voluntarily invested:
button: 2/6 = 1/3 pot investment
small blind: 1.5/6 = 1/4 investment
big blind: 1/6 investment.
This means that a total of 9/12, or 3/4 of the pot is accounted for in the form of voluntary investments. So 1/4, or 1.5 small bets, of the 6 small bet pot is basically up for grabs and will be distributed among the players depending on how they play postflop.
When they both call the raise, we see a flop and again we have investment opportunities and so do our opponents. If everyone is playing correctly, every bet will increase the bettors share in the pot, and every call will earn a profit. Some may hear this last part and think "but if my opponent is earning profit, that means he's taking it from me." which is partly true due to the fact that if they both fold to our bet, we earn ev of (pot) which is near impossible to improve upon without a near unbeatable hand. Instead, what really happens when we bet and get called is that we have reduced the profitability of the opponent's hand by making the bet, which claims the pot a fraction of the time, and which forces the opponent to put money into the pot for a return on investment that is smaller than the % of the pot that the opponent would earn by checking.
Here's an example, following the preflop action from the op:
flop K
6
5
small blind checks, I bet and it's on the button. If the button has something like T
9
, or 8
7
, then he can surely call profitably. Does this mean that he should be happy that we bet? Nope. If both blinds had checked to the button, he could have taken a free card and hit his draw for free. Zero investment + about 20% equity realization = infinite return on investment of about 1.2 small bets immediately upon checking, plus the possibility of improving on the river if he had missed. If we bet instead of checking with AKo, we reduce this profitability for the button: 1 small bet invested into the now 8 small bet pot = 12.5% investment with 20% immediate equity realization = 1.6 small bets - 1 small bet invested = 0.6 small bets of immediate profit for the draw on the button.
I know most of you already get this, but I needed to lay the groundwork to get to this point:
Your opponents will consistently have the opportunity to make profitable plays. This doesn't mean that you screwed up. It's just because cards have equity in the pot. We may manipulate the pot to reduce this profitability, but we don't get the whole pot in the long run. We just get a piece.
I believe that AKo, and many other hands, have this effect of reducing the profitability of the opponent's hands, thus I raise AKo preflop in the big blind without considering any other option vs limpers.