My reaction to that is: they did do it in a more modern idiom: that was Star Trek: The Next Generation, which I have heard was allegdedly mildly successful. If they honestly want to retain strong ties with the original, move forward, not backward and not retroactively. Trek isn't damaged enough to require a reboot.

Imagine if they had gone ahead with the Doctor Who reboot in 1996 as they wanted to. The Doctor and his teacher Borusa roaming the universe on a quest to find his Daddy.

I'm with those that think that if they really want to do something like this, they should just call it by a new name, not Star Trek.