Cdc- There are many class A amps available, though probably more tubes than ss versions. There is a theoretical advantage to class A amplification, but there is the efficiency issue. In class A/B amps, all voltage and driver stages (that I'm aware of) are class A. It's only the output stage that is configured for class A/B. There are amps with higher biased class A/B output stages that run up to 15% of their output power in class A; the brand Symphonic Line comes to mind.
Obviously, if you need lots of power, class A/B amps will likely be necessary because of the efficiency. However, for absolute sonic reproduction with the fewest compromises, class A operation is usually first choice.
Remember, class of operation alone won't make up for compromises in the quality of parts used to implement the circuit design. There are some excellent examples of good sounding amps in either class of operation, though to my ear they are usually tube units.
Some of the newer, true digital amps, (Tact, PS Audio, etc) use a completely different class of operation. They are extremely efficient, and have garnered some very high praise sonically speaking. I've yet to hear them for myself, but that is another option for you to consider if you need high power.
As for switcher power supplies, lets not forget about one of the truly innovative engineers in audio, David Berning, and his designs. Bob_b has already stated the facts concerning this power supply type. As Ezmeralda11 has pointed out, if you're really interested in learning the technical info of different amp circuit topologies, there are several good books on the subject.