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

Class A sound better? No, lots of factors to consider. You have first of all assumed Class A sounds better. Not always true.

Exactly.  I own four Class A amps so obviously like what they offer (aside from the heat and the electric bill), but horses for courses - some Class AB amps sound better in some systems. Generalizations like the original posts are meant to stir fuss, not logical response.

I use a Class AB tube amp in my main system as a matter of fact, and I prefer it with those speakers to the 100 lb. + Class A monos I used to use. OTOH I use a stereo Class A amp with some electrostatics and it is a great match.  YMMV

Gato Audio, a Swedish company makes AB amps that will compete with almost any class A amp. They now sell factory direct with free shipping. And best of all no sales tax. Steve Guttenberg did a review  recently.

It’s not true it’s not that cut and dry many very high quality amps may have the 1st watts say 20:watts in pure class A 
then switches to class AB.  That being said , inside the Quality of the parts have much more to do with the final result of the sound .
I owned a Audio store until 09 and Had many parts modded or  upgraded,for the vast majority of mfgs use average parts at best .
on average 25% or less of the cost actually goes into the electronics,the rest over head and markup. That's how 
Modwright was able to be so successful by putting in Premium 
parts in the most critical areas. Companies like Gryphon for example use top of the line puts throughout ,and are exceptional 
in sound quality.  That being said ,not everything is in               black and white. As well as the engineering  and their design .