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I would like to point out that in audio applications like quitar amps and mic preamps used to add “warmth” to voice, that even order distortion products that “are more pleasing to the ear” the superiority is not “alleged”. Since “more pleasing to the ear” is a desirable trait in those cases, the superiority would be actual rather than alleged if the even order distortion products are what is being intentionally sought.
In audio applications, spectral purity is not always what is desired. The judicious use of intentional distortion of certain types has been a part of the popular sounds of music for quite a few decades. To that end, some people try many tubes/valves, whether new or salvaged from older pieces of equipment to find ones that are “sweet” (ie, have the characteristics that person desires).
In other audiophile applications, it is not impossible that a given combination of tube amplifier or stages into a specific speaker may yield a sound that particular audiophile finds more pleasant to the ear, even though the total harmonic distortion may be higher than the clean signal that some solid-state devices could achieve. But the name of the game there is “pleasing to the ear” and is a subjective quality.
Now, if a tube circuit can theoretically make a more efficient output stage for part15 AM, for a small niche market it might actually be worth the bother to try assorted individual tubes of a specific until one is found that performs well, even though it might require a bit more filtering or fine-tuning of filters to surpress the harmonics.
Tubes are, as you pointed out, not of consistently good quality these days. They are a more primitive device in some regards than solid-state devices and less convenient to the current idea of drop-in no-fuss replacement. However, for certain audio applications they can be worthwhile if their sound is something one wants, and if they could be more efficient in the rf stage for part15 AM it may be worthwhile to some folks.
Probably the biggest question I’d have is how much more efficient *could* they be, compared to the solid-state devices typically used in currently popular part15 AM circuits. And whether that degree of possible improved efficiency would be large enough to offset the time and expense someone would have in making or maintaining a transmitter made with them.
Which boils down to an individual judgement call in the end as to whether it was worth it, much like it does in things like guitar amps and mic preamps.
Even knowing from years of using a tube guitar amp how finicky tubes can be and how hard it can be to find decent replacements and then readjust the circuit for the differences between even two tubes of the same type, I’d at least consider at it as a possibility. As Rich pointed out in the discussions on grounds as relates to towers and masts, radiated power is linear for a given system in that a 100 milliwatt transmitter can use a 250 foot tower as efficiently as a larger commercial tranmitter can. So if an option like a tube final output stage can deliver a greater percentage of the allowed 100 milliwatts into an antenna, performance should be better as regards range.
Whether the improvement would be worth the money (since tube gear is more expensive and time consuming to build), that would be something people would end up having to make their own judgement calls on.