I'm honestly not sure we'll ever see HD versions of The Next Generation, Deep Space Nine or Voyager. The images are just to soft and fuzzy for them to do a quality upscaling and the amount of reworking needed for the original film with new effects would be expensive. Plus we have no idea what type of shape the original film is in or if it even exists (completely) anymore.
The reason the picture looks so 'soft and fuzzy' is that it was transferred to video, thus making it SD. If you saw the film they shot, I'm sure it would be sharp as a knife.
There would be no upscaling from those video copies required at all. 35mm film is usually filmed and scanned with a 4k resolution, that's slightly more than 4 times HD quality. So they wouldn't have to do a thing as far as converting the footage to HD, in fact, by making it HD, they are actually degrading
the original image
While it's totally possible that someone was an idiot and 'lost' thousands of hours worth of film, I highly doubt it. It's not like the show is 100 years old...