Square waves are simply sine waves with all of the odd order harmonics added - it is not really DC at all. Once you add all of the even order harmonics as well, the wave becomes a saw tooth wave.
Think about it - this means that to accurately produce a square wave, it requires unlimited bandwidth - simply impossible in the real world and realistically, not needed when we cannot hear over 20khz.
Since any wave is made up of sine waves, as long as the amplfier can cover 20hz-20khz without problems, there is no reason why distorted guitars would be a problem. The difference in sound is most likely due to your ears.
Crossover/notch distortion that Class B (traditional Class B anyway) and improperly biased Class A/B amplfiers suffer from because a transistor requires a certain amount of voltage before it turns on - so the would be a notch as the wave crosses over from the +'ve to the -'ve or vice versa.

As far as square waves sounding terrible, remember beauty is in the ear of the beholder.
[ December 23, 2003, 19:23: Message edited by: Bassaholic ]