If watts is the only criteria, then it’s best to minimize watt costs. But we’re paying for sonic performance - amplifiers do not sound the same and do not perform the same. Lower noise floors like no-noise-black usually is the preview of costlier parts and engineering.
Seems your assumption that Class A is superior to others, but in reality it’s a personal preference and implementation. Not all Class A amps perform well at the frequencies extremes.
It’s common that additional headroom increases sonic performance. In other words, it’s best for an amp to loft along than to push them hard closer to their limits.
An example of non-class A excellence is Audionet’s Stern Preamp and HEISENBERG monoblocks that was designed by top German engineers with unlimited time and unlimited budget. The result was amongst the best sonic performance money can buy, and it’s displayed in the Smithsonian. By best means lowest undetectable black noise floor and sounds like real live instruments, provided the recording and the rest of the audio chain is up to the task including transparent speakers like Magico (I visited their factory, their cutting edge designs are based on measurements to minimize errors).
Not confident a headphone expert is knowledgeable about speakers, amplifiers, etc as headphone jacks do not perform the same as connection to speakers, especially top performers.
In highly transparent systems which are usually considered very costly, difference in cables is commonly audible, and moving up a product line one typically hears improvement. But with lower transparent systems, it’s much harder to hear differences in cables- so lower cost less transparent cables are a much better match. Sorry off topic, but your posts that any cable performs the same does not meet scientific measurements in cable design (like Iconoclast designed by a Belkin cable engineer and reveals on the Iconoclast website how and why the designs used using calculations and measurements) or the vast voices empirical evidence.