It's moreso that the typical tricks to clean up digital audio don't typically result in a fidelity increase unless the noise is particularly bad. If the square waves are visible and noise isnt sufficient enough to cause significant distortion in the output of the amplifier (by switching the transistor gates when they shouldn't be), then there likely isn't much of a performance benefit
But there may be an interference benefit.
Typically the "warmer" sound quality people refer to has to do with increased second order distortion
meaning that there are harmonics that are 1 octave above the media you are playing that are created by the tube, and people find these enjoyable to listen to
Class A isn't an awful technology but it is by far the most power consuming. It has the least distortion overall by a small amount, but in general the amount of power they consume is pretty significant.
Class AB amplifiers are typically what is used modern day as the distortion difference between class AB and A are going to be VERY minimal, I'd imagine hardly audible if at all.
Anyways, the reason I say that is that the tradeoff for using class A is significant power draw in exchange for truly great high-fidelity low distortion sound. I have no idea why you'd use a tube, because the whole point of going class A is to reduce distortion as far as possible. However, using a tube adds massive amounts (audible) of second order distortion, so one should reconsider why they are doing that design.
The other thing is that since class A amplifiers are so power consuming, a lot of power is dissipated in the switching element (tube) instead of the load (speaker). Tubes are not typically "high power" devices. A single LARGE tube in a guitar amplifier (EL34 for example) is 25W per tube, and a very large amount of that is burned as heat instead of going to producing useful output power. If you're looking for high wattage (which typically isn't the case for those who are making class A amps), class A is NOT the way to go, especially not for tube amps. High wattage tubes do exist in the form of Russian surplus but aren't typically super common like guitar tubes are, so sourcing components for high wattage class A amps will likely be prohibitively expensive.