The way the thermal constant works in a tube is unique to its construction. As a result when you saturate an amplifier built with tubes rather than getting square wave clipping (which is full of odd harmonics) you get a modulated overtone. In Music systems this overtone has energy at musically compatible harmonics and so it still sounds good. In radios it can be easier to filter out the spurs (spurious overtones from non-linear operation) without swamping the modulation on the signal.
The thing to note is that (good) tube amplifiers can be designed to be very linear until they're driven too hard - the audiophile community often overlooks this detail when they're shopping for "warm" tube amps for general power amp duties. The big differences between tubes and other kinds of amplifiers appear when they're driven at, and especially past, their design limits.
In an application like a guitar amplifier, some kind of effect/distortion pedal, etc the tube circuit is typically overdriven by design to get all of those warm harmonics. A tube that isn't being overdriven is every bit as capable of being a "wire with gain" as any kind of transistor or more modern circuit.
Liking tube sound or, more generally, the defects/characteristics of a particular amplifier (, headphones, speaker, room, ...) is perfectly fine with me.
I get easily annoyed though when people start spewing pseudo-scientific BS justifying that deviations are objectively better than no deviations or that there are significant (or "obvious with good ears") differences between amplifiers where there simply are no such differences.
You do understand that your point of view is only one among many valid positions on the subject, some held by authoritative figures? (and I don't mean me, I'm thinking the likes of JJ)
This isn't solely a defense of the position you challenged, more a call-out on your tactic here. You're not exactly representative.
The talk of transistor amplifiers being perfect and having no sound at all is of course nonsense: typically this kind of claim looks at frequency response and outright ignores slew rate, crossover distortion, behavior as the amp exits its passband on either extreme, and so on. There CAN be transistor amplifiers, both simple and incredibly complex, that are so good that they've got effectively no sound at all. It's even possible that it's easier to get there with a transistor amplifier given enough money and resources. But that's not the claim.
eventually you do get a square wave (similar to a transistor) but with less overdrive, you get a "soft clip" waveform that is rich in second harmonics. these harmonics are an octave above the fundamental, and can also create a psychoacoustic effect where you hear another sound that is an octave below. bass players LOVE using tube amplifiers for this reason--it really fattens up the sound without making it sound crunchy.
