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

Lower power consumption with most A/B amplifier designs. They tend to be popular in devices like DACs. Due to the nature of the Class A topology, they are very inefficient with electricity and typically generate a lot of heat. My Class A systems can only be run once or twice a week...otherwise my power bill will go up! 

Class A has a conduction angle of 360 degrees, whereas A/B is less.

In theory, this should translate to a more controlled and linear amplification of the signal. In most cases, Class A amps have more of a "grip" on the signal and can be "straight wires with gain." Everyone hear probably knows what I mean (see what I did with that spelling mistake) lol 

yep. So class A is superior if it is designed well without compromises.

Class A amplifiers don’t always sound better. It depends on the headphones or speakers you’re using. Headphones and speakers with superior transient response (able to keep up with and resolve complex music) tend to sound better with Class A. But not all are made equal. This means you could have a Class A amp that performs worse than a Class AB - although, if designed well and without compromises, Class A is the gold standard.

This is a great resource:
https://circuitdigest.com/tutorial/classes-of-power-amplifier-explained