This is a very good thread, but just to clarify; Class A is a single-ended amplifier. Push-pull is class A/B (even though it is often described as class A). Do I understand it correctly?
@sngreen No. The Dynaco SCA35 is an EL84-based push-pull amplifier that is class A to full output. This is so because both output tubes are fully class A, only operating out of phase with each other. In this way the amplifier generates lower distortion than would ever be possible with a single-ended amplifier, and easily has wider bandwidth (and more power) too. No downside, except for the heat.
We've been building class A push-pull OTL tube amplifiers that are class A for decades on now (nearly 50 years). Our largest model makes over 500 Watts in class A.
FWIW though, class D has seriously eroded any reason to go class A. The reason a class A amplifier can sound good is because of its distortion spectra, which tends to be more benign than an AB amplifier. However, the way the feedback is handled has a tremendous effect on the distortion spectra as well, which is why merely being class A isn't always enough. Feedback can be poorly applied (and often is), resulting in a harsh sounding amp with measurably low distortion, on account of non-linearities in the feedback loop introducing higher ordered harmonics.
A benign distortion product will be mostly the 2nd and 3rd harmonics, with enough amplitude that they can mask the presence of any higher ordered harmonics (the latter of which, if unmasked, are responsible for an amplifier sounding dry, bright and/or harsh).
Turns out that class D, if designed properly, has a similar distortion spectra to a really good class A tube amplifier, and sounds similar, since the distortion signature of any amplifier is also its 'sonic signature'.