The concept of the "TOS crew" have been there and done that for 50 years, what could an unknown set of new characters possibly have to offer?
A TOS/nu-trek script can easily mandate that Kirk and the Enterprise enters different galaxies, universes, time travel, get into war and conflicts, resolve them, and discover new life and perspectives and better themselves week in week out.
This is only assuming that all you care about is the plots, which by and large most people don't really give a shit about. People are drawn more to characters. Kirk & crew are good ones, but after a while it gets played out. Any kind of TV reboot would have to reimagine their characters to make them fresh and vital. A 50 year-old crew just isn't going to cut it on TV without some retooling.
For me, the interest in seeing new characters is just because I'm tired of Spock, Worf, or Kira. You can do spins on them, or just make new ones. But the new ones have to be good. You can't just throw in token characters like Mayweather and Kim. The problem with shows like Voyager and Enterprise was that most of the characters were too dull or unlikeable.
New crew, new ship, new adventures.
Drew decreasing ratings with every attempt after TNG.
But at the height of Trek oversaturation. If they had done a reboot instead of Voyager or Enterprise, and it was stuck on UPN, it probably would have declined just the same.
The success of the new movies I think comes down to these factors:
1. Fresh blood. The people working on the later shows/movies were obviously burnt out.
2. Giving it a rest. There was a time (albeit short) where there was no Star Trek, and no foreseeable Star Trek. It wasn't two shows and one movie at the same time, which makes Trek a little less special.
3. Sticking to movies and action. They definitely made things more exciting like Star Wars, and less like the stagnant Trek. It didn't hurt that they had far more generous budgets.
4. And lastly, of course the original characters and reboot craze. People eat that up... at the movies. TV is a whole different beast.