If we were confident the guy had no 5x or 44 then we should actually bet pretty large.

So if we assume that the guy has no combos of hands that beat AA then a small bet-sizing on the flop doesn't make sense. As a guide, having the nutted equity distribution often means big sizings can be good, even if we don't have enough nutted holdings to bet at a very high frequency. This is because we don't look purely at equity, we also look at the equity distribution. It can also be demonstrated that while there is a loose correlation between range-equity and betting frequency, it is rather straightforward to construct hypothetical models where we should check range despite having a huge equity advantage.

There are situations where it is correct to bet big with a range(equity) advantage and also small. Just so we are clear here, the sizing is not necessarily a function of the equity advantage.