I will start ;-)
Playing "On key" is not a matter of opinion - it can be measured with a frequency counter, and compared against the reference frequencies, and the degree of error can be determined - even if the observer / listener does not have a problem..
The importance of playing "on key" is a matter of opinion.. Vibrato is deliberate deviation from 'perfection' - And other forms of deviation from close compliance with the 'reference' pitches MAY actually sound more pleasant / musical / interesting to some listeners.. I think some of this is highly subjective and some listeners may hate a performance which others, for the very reasons which made the performance horrible to some, may love it!
It all depends on the music and the listener.. But I would agree if it was said that the ABILITY to play the 'intended' frequency should be there for a player to be regarded as good - regardless of whether this frequency is at a 'standard' musical interval.
Taking this further - Someone who plays and does not hit recognized intervals, BUT is capable of repeating the performance accurately enough that the piece does not change noticeably (or unpleasantly) can be, in my opinion, as 'good' as someone who can play "the swan" perfectly on-key.
If one is ONLY wanting to use the Theremin as a replacement for some other instrument, and play ONLY pieces which depend on intonation for their structure, then I would agree that "correct" intonation was of paramount importance - But in such cases I would question the rationale of using a Theremin.
To me, it is the "ERRORS" in intonation which make the sound of the Theremin more interesting.. It is listening to the subtle correction of pitch, and the freedom of expression this creates, and how this imparts a component to the sound which is exclusive to the player.. If playing was perfect, it would be less interesting - and one would not have any way of differentiating one good player from another.
The fact that the same piece played by 3 different GOOD Thereminists, will still sound ENTIRELY different, is due to "ERRORS" in each of their performances..
Lose the "errors", aquire "perfection" and, in my opinion, one may as well relegate the Theremin to history - because no one will be interested in hearing it!
Who would be mad enough to choose the Theremin if "perfect intonation" was their primary concern?