Why are most High End Amps class A

And you're correct in the assertion that increasing bias doesn't improve the problem, it just increases the signal level at which it occurs.

But it does reduce the audibility of the problem. You now have distortion only when the output signal is very high and you have no crossover distortion (GM doubling or whatever you like to call it - lets say transition distortion) when output signal is very low and it runs in Class A (both sides conducting).

A small absolute amount of distortion on a large signal is better than the same absolute distortion on a small signal.

In one case the listener may notice the transition distortion (large part of the overall signal) while in the other case it will be much less audible due to it being a smaller proportion of a much larger signal.

You now have distortion only when the output signal is very high and you have no crossover distortion (GM doubling or whatever you like to call it - lets say transition distortion) when output signal is very low and it runs in Class A (both sides conducting).

This is quite correct, but the gm-doubling transition distortion is much worse than the crossover distortion. So as to audibility . . . it all depends on the application - each road has its burdens to bear.

A small absolute amount of distortion on a large signal is better than the same absolute distortion on a small signal.

I've heard it asserted that crossover distortion manifests itself (it drives THD upward) more as the signal level is reduced . . . and honestly, I'm not sure whether or not it's true. It seems to make intuitive sense, but I've measured lots of amplifiers, and I'm doubtful as to whether or not the measured data supports it. Complicating the issue is that THD+N of course rises in a linear manner with a reduction of signal level . . . but when you measure just the noise, you get the same results.

I think it may be that as the signal levels are reduced, the proportion of the total signal that's in the crossover region increases, but the crossover non-linearities are at the same time being spread out across a larger proportion of the waveform, making them less severe. Whether or not these opposing factors cancel each out is the question, and I certainly haven't the skill to investigate it with pure mathematics, and my current measurement equipment isn't sensitive enough to find the answer emperically.

Shadorne - tests show that underbias and overbias causes increase in distortion (especially higher order odd harmonics) for all signals (in wide range of output power). Increasing bias above optimal level increases non-linear area (of non-constant gm-doubling) and makes it worse.

Proper way to do it is to bias it into class A so nonlinear area would never be reached and gm doubling would appear constant for all signal all the time. Unfortunately this requires (typical) bias of 150% of anticipated max output current. At least that's how I understand it.

tests show that underbias and overbias causes increase in distortion

Agreed but I don't understand the point? Of course you have to match the bias precisely between both sides as otherwise you'll get loads of higher harmonic distortion. However you can design circuits that help achieve this and help maintain this under various conditions - it all boils down to careful topology.

Shadorne - careful topology is always important but I think that as long as transconductance in biased area is non linear extending this area doesn't alleviate the problem but makes it worse (extends nonlinear area).

This problem is different from crossover distortions or switching distortions. Of course huge amounts of negative feedback will make everything nice and linear but for the price (TIM) and even then still not as good as class A. The only strength of class AB is that it costs less and therefore better quality amp (power, parts etc) can be made.