Contrary to what angry YouTubers might think, Kurtzman is doing a satisfactory job running the Star Trek franchise, otherwise he really would have been fired long before now. It would be foolish for a new regime to clear out someone already overseeing the franchise rather successfully just so they can have their own people take over when there is already someone doing the job quite well.
Besides, Berman didn't leave until all his Trek productions came to an end and the only reason Abrams left when he did was because Disney recruited him to work on Star Wars. Kurtzman's Trek productions are still going and he's not being scooped up by any other studios to work on their successful IPs, so don't expect him to leave anytime soon.
