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.

Well, I have had some quite powerful small Class A/B amps which deliver 2-3X their rated power. Not only that, but they are about 3X to 5X as powerful on a wattage rated basis as many solid state amps.
The earliest amps to sound super dynamic is the McIntosh MC30s. Next are my highly modified Dynaco’s which can deliver huge and clean bass dynamics into low impedance loads. Lastly, my custom built Altec transformer based 130 watt amps which could drive anything a 500 watt solid state amp can. Maybe my Class A/B amps aren’t as refined in the mids as the best Class A tube amps I’ve heard, but I can put my hand on my big amps transformers hours after being played hard while I could burn my hand in 15 minutes anywhere on the chassis of an EAR 890 70 watt Class A amp which can’t handle low impedances.