Should I buy a Class A Amp.

Atmasphere I've never heard one of your amps (I live in New Zealand) but from what I've read they would indeed do just as well on rock as on classical or jazz. Same with the big Pass amps. They're very expensive though, and when you get down to the slightly compromised amps there are trade-offs that mean some are better at rock than others. Bass and PRAT are essential for rock and some amps just don't deliver because they have other priorities. 

Could it be said that Class A amps, like Pass for example, play better on certain types of music? Better classical than rock, for instance?

Not really. The requirements of an amplifier do not vary according to the music. As I said before, the idea that an amplifier can be suited better for a certain type of music is a myth. From a designer's point of view there is no way to approach that.

Even if you have a tiny SET power amp, if set up correctly it will not favor a certain form of music. You might find if its not set up correctly (the usual problem being that the loudspeaker lacks the efficiency needed to really allow the amp to sing) that it might seem to favor less dynamic material. But that would be simply because of power limitation and not because the music was classical or jazz as opposed to rock. Rock can be quiet and delicate too.

The fact of the matter is people express taste in music and electronics do not as electronics don't have a brain and can't express taste like humans.

when you get down to the slightly compromised amps there are trade-offs that mean some are better at rock than others. Bass and PRAT are essential for rock and some amps just don't deliver because they have other priorities.

Bass and PRAT are essential for classical and jazz too- that is something universal. Now some amps have colorations- for example transistors can be bright. That does not help rock any more than it helps classical or jazz or folk. Tube amps can be overly rich. That does not help rock any more that it helps classical or jazz or folk. 

The only exception I can think of is actual instrument amplifiers like a Marshall or Fender, where the character of the amplifier becomes part of the 'sound' that a guitarist is trying to create (often with the assistance of effects pedals). As audiophiles we are simply playing recordings of such, so that really does not seem to apply here.

This particular myth dies really hard BTW. But it is a myth! Amplifiers are designed with mathematical formulas which are not capable of expressing musical taste. If I can put this in perspective, someone asked on this website once if there was a speaker that favored mid1980s downtempo music. You might not really get what that might be (early Clan of Xymox?? Stuff on the 4AD label??); how in the heck are the electronics going to favor that over something a little more up tempo or recorded a few years earlier or later??

The answer obviously is they can't. In all cases you just get the best combination of electronics you can afford and hopefully it all is matched well enough that you can enjoy listening to it for some years.

My amp sounds better with some types of music than others.

I base my findings on empirical evidence and what I hear, not on theory.

Nothing mythical about that.

Tim,

As they say, just because I don't know how to cook doesn't mean that I don't know how to eat.
If I hear the difference I hear it. Just because someone has ideas of what I should or should not hear doesn't change this.
Ralph's tone is often egocentric and condescending, and I believe he knows it. I do not question the quality of his amps, by the way, I never did. But I will leave him alone from now on.
So, yes, to state it again - I would not choose Kondo for jazz/rock and I would not choose Rowland, Pass or perhaps even Lamm hybrid for acoustic guitar music. I would choose tube amp. Which one? I don't know, I would listen to them all above certain level. But usually we have to choose just one, along with one pair of speakers, for many different types of music. My current amp is actually better for jazz/rock than acoustic guitar but not bad for anything. And speakers are the other way around !  However, it's a modest system by audiophile standards.
Let's just not simplify and distort things.