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

Idk...my sugden A21se single ended class A sounds wonderful to my ears. Probably the best I’ve heard thus far. It somehow is adding something to the music that, at least to me, sounds more natural or organic. Maybe its in the design, maybe its added distortion...who knows? All I do know is that I’m either hearing or at least perceiving a noticeable difference in a good way. This is not to say that my Marantz pm14s1 sounds worse in any way, I’d rather say it sounds different. I will say that the sugden does seemingly run out of some breath at very high volume, where as the marantz seems to have more headroom. However, at a lower volume (where I generally listen), I gotta give it to the sugden. It is doing something right that makes me me want to keep on listening. Its a beautifully designed amp by the originators of SS class A, since 1968. Countless reviewers of the A21 have felt the same way about it as I do, so I don’t think I’m nuts. Is it the absolute "best" amp available?? Of course not!! However, for what it costs and what it does do, it does a darn good job. No bells, no whistles, no dac, no phono stage, no digital whatsoever, All Amp... Also not sure why people harp on how hot it gets..its class A! Always on, always ready. If I want to pay a higher electric bill, so be it. There are some much older a21’s still in use today with zero issues, despite the heat.
https://en.m.wikipedia.org/wiki/Sugden_Audio#:~:text=In%20April%201968%20the%20A21,amplifier%20under....

you boys need to play nice....the concept of "which is better" is such a competative, guy-thing....listening to a system is about pleasing the listener; I hope we all recognize there is no "absolute' sound in reproduce music, and ones perceptions are subjective ...we should recognize that some "distortions" are "pleasing" to certain listeners. And some listeners cannot get past preconceived biases, and hear what they want to hear.  At the end of the day, it is all about what pleases the listener.  I know full well that my room is a serious limiting factor for my sound and I simply have come to accept that....as it stands, good source material sounds wonderful , to me, and that is what matters, I believe....I am not here to "compete" with others.....ENJOY ......

Class A amps (almost) always measure better,

Also not true.  AB can have vanishingly low distortion. Compare for instance Pass' class A designs.  He deliberately designs for euphonic distortion.  He does not make absolutely low distortion amps nor does he wish to.  It's exactly his house sound.

So, neither sound nor measurements are better universally by class.  Class D for instance can best many Class A for distortion and low output impedance. Not always though.

What is true is that the crossover distortion vanishes with Class A.  Sound quality, output impedance, distortion, all vary greatly and overlap with other class of amps. 

Hear, Hear... jw944ts! 
I have, after almost 50 years in this wonderful hobby, ended up with "mostly" tube equipment, push pull A/B, with Martin Logan hybrids and auto formers (take it easy georgehifi, my preference, my system). Sounds great to me (and associates).
My best friend(s) have older Morrison mono class A SS amps, with Morrison (new model) speakers. Sounds great to us.
Our other friend, has Mark Levinson 300w amp and some European (German) stand mounts. Sounds Great.
I think the point here is that, yes, there are general "rule of thumb" guidelines but.... there are no absolutes (class A is superior.... etc). Way too many variables and always an exception to "the rule".
My take on all this... that it is a valuable endeavour  to mix and match, swap equipment in and out, socialize and listen to music (and gear).
As jw said...ENJOY....

Seems to me that everyone is addressing the question solely with regard to SS amps. Ask the same question about tube amps and I think it would be generally agreed  that a pure class A SET will win out over a class A/AB push pull triode as long as they are matched to the right speakers.

J.Chip