Why do we steal with Axs?

[Johnes Benjamin]

First of all, I don't know how the set vs Axs debate got going. The question was why do we raise it, and the answer is the same for both. FWIW I prefer a PP, but whatever.
We raise hands like Ax because playing a pot in position against the blinds is a good spot to be in.

You are absolutely right that 72o can play out the same if we are just folding people out, and that is why good players are very loose and aggressive from the CO and BTN.
We play Ax more than 72o b/c we are more likely to make the best hand, and we can't expect to fold out the blinds every time.
We play Axs b/c it is slightly better than Axo
We play PP b/c they are often the best hand to start and flopping a set will almost ensure they are the best hand.

One more small thing is that having an A in your hand doesn't just mean that you have a strong hand, it means the blinds are slightly less likely to have an A themselves, and therefore be slightly less likely to have a hand they can call a raise with

You are correct in stating many of the points (such as Axs vs Axo) are small differences, but poker is about getting as many small edges as you can.
I remember a high stakes limit player saying he won about 55%. He was rich b/c of that 55/45 edge.