Should Amps be plugged into a power conditioner?

IME, amplifiers are far better sounding when plugged directly into the wall. You trade off filtering for much more headroom. I will take more headroom all day long.

I should add that I have always used higher powered amplifiers. This may not be true of tubed or SET amps as I have no experience with those.

Depends upon the amp and the conditioner.  Conditioners that allow many amplifiers to function without limiting the headroom are very expensive.

The amp's class of operation could be a factor, e.g., class A, AB, or D.  Any knowledgeable opinions?

For me better safe than sorry. Panamax had been my best equipment "shepherd" and protector since deep early 90's and never failed even with STRONG surges. Never cared to upgrade that one.