"The Question: What is the tubes effect on the tone? (amp tube, not instrument tube) Is a perfectly clean Theremin tone desirable?" - Rohbiwan
First, Welcome to TW, Rohbiwan!
Ok, first - When it comes to opinions on what is "desirable" from a theremin tone, well - you will not get a common answer to this question anywhere.. Opinions about the "best" or most "real" or "authentic" tone are as mixed up as the people who play these instruments.. Musicians are generally more mixed-up than the general population, and theremin players (and developers) well - we are all completely mad! ;-)
So all I can give you is my personal opinion and ideas about theremin tones and tubes.. These opinions are no more valid than anyone elses, and probably less valid than many because I live in an isolated technical bubble, dont really play, and meet a musical person once every few years if I am lucky... LOL ;-)
The tone from a pure theremin (here I am taking about true analogue distortion-free multiplication for heterodyning), if not processed or distorted internally or externally, is generally sineusoidal and (IMO) boring. Most theremins apply liberal doses of distortion (usually on the audio signal - but in many cases at the mixer, and in some cases by distortion of the HF oscillator waveforms) and IMO it is the care in the selection of distortion mechanisms which determines who the sound will please.
Further distortion can be applied to the audio signal after it has exited the theremin - and one of these possible mechanisms is the amplifier / speaker.
I believe that one thing which adds "warmth" to the tone (gives it an acoustic quality) is microphonics - as in, the sound from the theremin causes mechanical energisation (vibrations, resonances etc) which somehow feed back and/or modify the actual tone produced by the theremin.
I believe that tube microphonics is the primary mechanism which makes tube amplifiers sound "warm" (not just for theremins, but for everything) - and that the soft clipping behaviour of tubes further enhances the sound in some cases.
Fred.