I don't know that the "fresh approach" was the draw for the movie. That assumes that the audience was made up of people familiar enough with Star Trek
that they'd know whether the approach was fresh or stale.
Abrams made a movie that was well crafted to take advantage of the expectations of the general global audience for summer tentpole action franchises. It focused on the franchise's most well-known names/images (Kirk, Spock, Enterprise) and was marketed as slam-bang exciting action that could be appreciated by people who'd never seen one minute of Star Trek
before, just like Iron Man
and The Avengers
appealed to people who'd never read those comics (and had to, in order to be profitable movies).
None of this has much bearing on a TV series, which has entirely different constraints and exists in a different industry - smaller budget, the need to produce at least 13 episodes per year, not two hours every three years, and the need to appeal to the audience of whatever channel it ends up on.
The only connection between movies and TV is that the movies represent a huge PR boost for any TV series, and that's the overriding reason why a TV series might take place in the same continuity, or at the very least, give us no indication that it's not doing that. The odds against any TV series, particularly live action, are so severe that I don't think they can afford to snub anything that will help boost ratings and also boost the confidence of Les Moonves, who is no fan of Star Trek
and seems content to keep making cookie cutter cop shows, sitcoms and reality TV.