I don't see Paramount striking 4K prints for any of their catalog movies until there's a proven market for them.
A lot of studios have done them already. Fox, for example, has a 4K master of
The Abyss sitting in its vault and has had it there since 2009. Pretty much all of Fox's 65/70mm films are ready to go in 4K, as well. Fox has gotten extremely stingy with its physical media releases, however, to the point that it's effectively ended Blu-ray releases of its television shows outside of the biggest performers.
I'd expect Sony's first UHD releases to be better, given that their first round of digital downloads included
Lawrence of Arabia and
It Happened One Night.
Paramount, though, has never seen
Star Trek has a huge money-maker outside of its new emphasis on the JJTrek films, and so yeah, I doubt we're going to see any real effort to remaster a bunch of films that will probably never make a ton of money. It would be
nice, because the existing Blu-rays of the original six films are downright hideous, but I'm still not holding my breath.
But this whole thing is putting the cart before the horse, considering almost no one is actually broadcasting or streaming in full 1080p even now in 2015. You can't find "full HD" on television right now, and yet the studios are hoping that
this will be the nut that cracks the shrinking physical media egg.