And you still claim to have passed your RAE? - you're talking about TRANSMITTER rf stages, NOT receivers, where everything is class A.
Transmitter wise FM uses class C multipliers and output stages, AM 'can' as long as you use high level modulation on the final stage - SSB must use a linear amplifier, doesn't need to be pure class A (which would make no difference), but it MUST be linear. If you use low level AM modulation, you require linear stages as with SSB, and for exactly the same reasons.
Again, that's transmitter, not receiver - where your receiver has a class AB output stage, like probably every other one, and makes no difference whatsoever.
You claim to have the ARRL handbook?, try having a look at it!.