A/AB IS THE WAY TO BE.
If you are talking about solid state, the problem you are up against is linearity of the circuit. Class A is used to help improve linearity, but a very real problem faced by audio designers these days is the semiconductor industry would rather not make linear devices.
So as a result unless one is very careful, feedback has to be implemented in the design to cause linearity. The problem here is twofold: first you have to be careful to not introduce oscillation by exceeding the phase margin of the amplifier circuit. The second problem is a lot trickier- you need to have about 35dB or more of feedback in order to prevent the feedback itself from adding distortion of its own (which tends to be highly audible as its mostly higher ordered harmonics).
To that end you need a lot of something called Gain Bandwidth Product, which to feedback is a lot like gas to a car: When you run out of it there's no more feedback. Put another way, the feedback is gobbling up gain in the amp and this gain has to be sufficient to allow the feedback to do the same job at all frequencies. I'm really oversimplifying this issue but that is because its a very tricky engineering concept.
For decades GBP has been sufficient in the bass region, which is why solid state has a good reputation in that regard. But its not been so good in the mids and highs- most amps made in the last 60 years have less and less feedback as frequency goes up, causing brightness and harshness as that is how the distortion is perceived. Incidentally, this is why distortion is usually measured at 100Hz. If distortion were measured also at 1KHz and 10KHz we'd have a far more accurate picture.
Class D offers a rather elegant way around this by allowing you to impose so much feedback that the amp's phase margin is exceeded, and so it goes into oscillation. The oscillation is then used as the switching frequency, thus killing two birds with one stone. Now you can have in excess of 35dB of feedback so the feedback can clean up after itself. In effect a class D amp is more likely than not to have lower distortion than traditional solid state amps (class A or AB). Its also impervious to weird speaker loads causing it to oscillate because its already oscillating!
Its very natural for a class D amp to make significant lower ordered harmonics due to how dead time and the encoding system make distortion. The result can be that those lower orders can mask any higher orders, resulting in an amplifier that sounds very much like a tube amp but with dramatically lower distortion and therefore more neutral. In addition its output impedance can be far lower than traditional A or AB amplifiers, allowing it to be a better voltage source.
So put another way A or AB isn't always the way to be.
