What are the advantages to a Class A amp & what are the trade offs?

@koestner I would say that this is a better metaphor:
class AB is like having a car with 2 engines and 2 gas pedals. Every few seconds you have to switch pedal and try to hit the same rpm again (we can pretend that the engines would overheat otherwise).

You hope that the engines are not different in strength or something but it is still hard to do the continuous switching without having a little bumpy ride.

Not to be argumentative, but don’t you think that the interface between class AB amps running in class A going into class B is not rocket science and has been perfected years ago? 

Grandstanding a bit, I would guess the majority of great SS amps are class AB, based on sales.  Just an assumption on my part.