Why would anyone want class AB amp when class A always sounds better ?

Yes, they are sometimes applicable.
Miller, what's wrong ? Give us an example. I'll give it myself. Gryphon Diablo 300 class AB integrated sounds better than Sugden class A integrated. But it's not a fair comparison, not what I mean, of course.

It's also often that current matters no less than wattage, at least.

As a direct example, some feel that the Luxman 509X class AB at $9.5k sounds better than the Luxman 590axii class A at $9k. Can’t get much more absolute-busting than that. Same company, both integrateds with same features, essentially same price, both current products.

Other than seeing the operational state of A or A/B on  a scope or test equipment, no one can "hear" such conditions.

A  "matter of fact" from the wisdom is needed  to clarify my unqualified babble based on taking 101 electronics decades ago. 

Clas A amps DO NOT always sound better.
They should in theory perhaps but this ain’t theory now is it?