Inevitably any new series will adopt something of the times in which it is filmed, not only in terms of the wider society but in the smaller sense of changing tastes, styles and production values. TV has moved on and a rehash of TNG would look outdated.
Where any new series would be judged for me would be in the spirit of the show, does it merely entertain or does it have us asking questions and thinking for years down the line?
We can't expect the franchise to remain stagnant, but nor does that mean it must be diluted in terms of actually being the thing it claims to be. This has long been my issue with the abramsverse. It's not that it looks different, or has new actors, or CGI, or lens flare (well, ok maybe just a bit there), but that it has rejuvenated the financial and commercial aspect of the franchise by sacrificing the very things that made it worth saving. Maybe on the small screen the emphasis will shift away from the spectacle and towards the content.
Arguably we are in a golden age where it come to non episodic story telling on TV, an era ushered in by the likes of Lost, 24, Prison Break, Green Wing and many others that may actually work in trek's favour come a new series. Quite simply the expected quality from small screen productions has gone up in the last twenty years in ways that aren't purely down to visual spectacle, unlike Hollywood which to my mind has become increasingly vacuous.
I imagine a new series may approach the issues of the the Middle East, mass immigration, terrorism, in the way the TOS approached the Cold War, TNG approached the Reagan era.
My own preference would be to move towards the small and away from starfleet. We could see the world through the eyes of a private crew, displaced civilians, even aliens. One thing we have pretty much missed throughout the franchise is seeing the Federation as antagonists. The galaxy must be absolutely full of dissident and seperatist groups that resent the growing hegemony of the Federation. The Maquis can't be alone in this. So how about pirates, privateers, smugglers, operating on the fringes of the Federation, faced with the consequences of events we have seen in other series?
