^^ They're getting close, but maybe another 5-10 years away... that being the ability to realistically material map one person's face on another in a video context. The trouble with old footage is that you don't have a complete 360 degree fixed axis video montage of the characters (especially the secondary ones) along with a full compliment of facial movements (e.g. everybody smiles differently). But it may be possible to interpolate enough to construct plausible facial movements. That's just the head... Then there's the complexity of bodies. You'd have to find a stunt double with the same body frame who can imitate the original actor's movements. Finally, you need a voice. I think that technology is even further out, that being the complete phonetic simulation of another person enough to construct new speech with the original voice.
It's a lot of work for the extent of people that would want to see it today... at least at this point. Who knows what may happen 20 years from now. Maybe there will be a huge Star Trek nostalgia wave and some enterprising movie industry people will make the attempt to create new episodes with believable facsimiles of the original TOS crew.