If I can be honest, the tos movies aren't exactly a good example here...
They weren't meant to be the exclusive example. There are many other instances where a series has changed hands, yet still had later movies turn out well. For instance,
Thor: The Dark World had a different director and writers than
Thor, and
Iron Man 3 was from a different director and writers than the first two movies. There are no doubt other examples. The whole point of an example is to represent a larger group of items.
Abrams' reboot was conceived as a series of movies linked together (might be wrong, but the old movies were never really conceived being like that, anyway) and thus this movie is supposed to be, after all, a sequel of the first two and part of a trilogy.
But concepts evolve from their initial form. That's not a bad thing. If every writer's first idea were their best one, then writing would be one
hell of a lot easier, let me tell you. Usually it's the other way around -- your best ideas have to be earned by slogging through a lot of trial and error and refinement and rethinking. So there is no sense in having loyalty to the earliest version of a creator's plans. Usually that's going to be the worst version, not the best.
Anyway, why are we so addicted to trilogies? They're not the only valid form of storytelling. Just because they're the popular formula, that doesn't mean that a trilogy is automatically a superior story to a duology and a standalone.
It seems to me that the goal of the Abrams films was to do an origin story showing the growth of the characters into the people we know from TOS, but that specific arc was not necessarily meant to follow a predetermined path over three movies. If anything, it's always seemed to me that the '09 film rushed to wrap up that arc by the end of the movie (since they didn't know whether they'd actually get the hoped-for sequels), so they created the implausible situation of Kirk getting promoted to captain just days out of the Academy; and then, in response to audience complaints to that implausible conclusion, they wrote STID in a way that would address that problem by having Kirk learn that he wasn't ready for command, but having him earn greater maturity and judgment over the course of the movie. (This is what I mean about writing being a process of trial and error and correction. A plan that doesn't change is a plan that can't work.) So that stretched the arc out from one movie to two.
But now I don't really see any need to drag that out for a third movie. The crew is in place, and they've started their 5-year mission. It makes sense for the third film to be an example of the mature crew undertaking that mission. That's the payoff to what the first two films set up.
and my point is that with a new creative team, the movie might feel too different and ignore aspects I liked in the first two.
It might; or it might introduce other elements that you will love. The unknown offers both positive and negative possibilities.