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

The build quality and engineering skill has everything to do with the end results.
pass labs, class A monos , Coda 16  amp just as a sample just in the U.S  alone.
In Europe Denmark makes several superb class A Amps , as well as classA-AB amps . For power hungry maggis you may need a Big power amp in Class AB 
there are even. Excellent ClassD amps and hybrids that sound good 
and many lower powervacuum  tube amps are in class A up to around 20 wpc and sound very good ,each amp has its own sonic signature.
your speakers have Everything to do with the requirements of your amplifier
and what sound you prefer.

Class A runs very hot and very inefficient , big watts in pure class A is big bucks .
that's why excellent amps ,integrated like Coda give you that option how much bias into class A ,my CSib integrated is close to 20 watts into pure class A , before going to class AB seamlessly to 150-300 wpc If you speakers are fairly efficient 
the amp rarely would ever leave pure class A .

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 .