I'm not so sure this kind of superfast reboot is anywhere near as omnipresent in hollywood as you seem to think.
There were five years between Spiderman 3 and Amazing Spider man, and that reboot was a business necessity to keep sony from losing the rights to the character. Also five years between Ang Lee's Hulk and the Incredible Hulk (which wasn't made because anyone felt a desperate need to reboot the Hulk, but because the brand new Marvel Studios wanted to establish a wider shared universe using the most famous heroes they still had the rights to). There were seven years between Superman Returns and Man of Steel, and that reboot was necessitated by the fact that DC needed a bigger superhero movie presence to compete with the MCU and had huge difficulty getting anyone other than Batman or Superman off the ground. It was ten years between 'Planet of the Apes' and 'Rise of the Planet of the Apes'. Eight years between batman and Robin and Batman Begins. Eight years between Rise of the Silver Surfer and the upcoming Fantastic Four.
Every other major reboot I can think of off the top of my head (from the last few years) has been of films already decades old (Robocop, Dredd, Mad Max, Red Dawn, etc).
Generally speaking, i'd say this 'modern culture of fast reboots' is completely mythical, especially in terms of putting a date of only 3-5 years on it (even the quickest reboots I know of were all at the highest end of that scale), and in so far as it does apply at all, it mainly applies to comic book movies which are based on a long history of reboots anyway, and constantly mired in a problematic web of who has the rights to what and how can they keep them.
I seriously doubt Paramount will automatically feel the need to reboot the series right away. If the new movie is a bigger hit than expected, they may simply continue it, although their committment at the moment doesn't seem all that solid. If they don't continue this series, they probably won't do anything with Star Trek for a few years. Hopefully, if they then decide to reboot it again they'll go with a solid new tv show rather than movies.