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.