In any case, I think casual audiences could eventually care about a series if it were well-written and featured interesting characters. People learned to care about the cast and crew of The Next Generation. They could learn to do the same in the last days of the 24th century.
They could... but then the question becomes why? Why try to get the audience to care about new characters when there are already characters people care about in the public consciousness?
And why continue Berman-Trek, which was simply one variant vision of Star Trek, largely created by other people? Is the point to tell an interesting story in the Star Trek setting, or is simply about maintaining the illusion -- or delusion -- of a larger continuity among all the different Star Trek series and movies -- that Star Trek is somehow real
? If the point is the latter, then it quickly becomes, IMO, a geeky-ass waste of time.