Frankly applying pitch correction in a theremin should not be any more difficult than for the voice - in fact it should be a lot simpler. The voice is a heck of a lot more complex instrument. The theremin is simply a static oscillator that has ultra-dynamic pitch control. So the uniqueness of the theremin is all about that dynamic pitch field - but the voice also resides in a fluid pitch field. The difference is that the human brain is directly connected to the vocal cords so it has a lot more (and quicker) control over that dynamic pitch field than a hand in the air disconnected from the sound source. But the base theremin waveform itself is ultra simple compared with all other non-fixed pitch instruments where there are complex stochastic things going on all the time (like lips vibrating in a mouthpiece, a bow constantly slipping on a string, or a vibrating membrane or vibrating vocal chords, etc). These small random changes create much more complex waveforms than a theremin (or any other synth that does not apply random control elements of some sort).
I've done a lot of experimenting with pitch correction on my theremins and Theremini and with today's programs that let you finely adjust pitch on the microtonal level while also maintaining vibrato all on just about any time-slice you like, I can guarantee that no one would be able to tell if a theremin performance had a bit of pitch correction applied here and there. Just as no one can tell these days if a vocal line has a bit of pitch correction on it. The key phrase here is "a bit".
Of course if you keep pitch correction constantly on and try and correct everything then yes you will likely be able to tell pitch correction is applied - if the original performance is way out of tune. In that case you will be able to hear pitch correction artifacts. Same goes for the voice. Pitch correction is ideally meant to correct a good performance, not fix a miserable one.
Now the Theremini does do a good job of applying its pitch correction algorithm when you look at it on a scope. The Boss pedal seems to do something very similar. And as I've stated before, if you put too much pitch correction on something it becomes an effect - which may be nice but not what is intended. So if you apply a bit of pitch correction on the theremin, I've found it doesn't really make it that much easier to play musically. What it does do is make it easier to hold tones for short periods which might be going way out of tune otherwise for a beginner. When you apply pitch correction you should try and hold your hand perfectly still. On a non-pitch adjusted theremin this will still wobble as it's impossible to hold perfectly still. But with a bit of pitch correction you can set it to a point where a single note comes out for a position your mind thinks is perfectly still and as you try and move your hand slightly you will hear pitch move. That's where I try and set it. You still get all the portamento you want as you are not really correcting to a fixed scale system, just trying to minimize very small motion changes. You still have complete vibrato control in a microtonal field (it's just slightly degraded).
From my experience, this can and does make it easier to play in tune - though not that much easier to play musically. And yes, it comes at the expense of a light degradation in the dynamic pitch field - but I contend not enough to distract the listener from thinking its a real theremin performance (assuming its a good performance). Maybe 10 people in the world might be able to tell a difference - and if there is an accompaniment likely few would hear it or care.
So I don't think the issue here is: should pitch correction be used? I'm sure any thereminist releasing an album for sale would be more than happy to correct a note here or there that is so out of tune as to be distracting - and we all know this can happen to any performer, no matter how good. I also think SLIGHT pitch correction is a great aid in learning how to play and as you get better you can pull back that correction. This was the goal of the Theremini and frankly I think that function of the Theremini does what it was meant to (but of course the marketing lingo may well mislead - as the Theremini is still very difficult to play with partial pitch correction on - and impossible to play with full pitch correction other than for stepwise melodies matching the scale you have set).
Frankly, I'm waiting expectantly for Dewster's creation - as from all the posts it promises to be a very exciting development - especially adding that formant function. But from the pitch perspective on the musical end, I want to see a theremin with dynamically changing waveforms (yes they change slightly on some instruments now but not enough in my mind). This is now done on synths all the time with wavetables - an area the Theremini tried to delve into but did not put in enough functions or flexibility (including dynamic ADSR control and dynamic wavetable adjustment and ability to load your own wavetables). Those functions would make pitch correction a lot more complex.
By the way, this is going to create a bit of controversy, but there are some thereminists out there that play so well in tune, to my ears it takes away from the performance of certain kinds of music (unless it's modern or very old music that sounds better without a lot of vibrato). I like playing that is expressive and just on the verge of being in tune for certain types of music (i.e. romantic music). So there is also a need for a device that will throw a performance slightly out of tune forcing the thereminist to use more vibrato.