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

For what it's worth, I have two Class A amps, a Reference Line Silver Signature (modded by Roger Modjeski, RIP) and a Plinius SA-103 (heavily modded by Vince Galbo Designs). Both put more than 100w into 8 ohms. I used to have Bryston 28B SST2, an AB amp that put 1000 watts into 8 ohms. I had all three amps at the same time, so I could easily compare them in my system, which includes PMC IB2i speakers (known to love Brystons). The class A amps sounded better by pretty much every parameter. The Brystons are long gone. What's more, the Plinius has a button you can press to switch the bias from AB to A. Class A sounds better, by no small margin. Again, FWIW.

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

The statement is just partially true. Some ears like class D over anything else... oh, and it’s genre related too

I like what ARCAM did with their AVR 850 with their class G technology.  Great design.  I would imagine the big concern would be the heat factor.  AB is a good compromise.  

Rarely an acceptable compromise, it would seem

The lowest distortion amp in existence is class AB. The problem with this amp is it doesn’t have any low-order harmonics to help mask any inadequacies in upstream gear or the recording.