If nothing else, I'm not clear how this would work as a series logistically without serious retooling.
Retooling is a given when you're adapting a movie concept to an ongoing series. Naturally you change whatever you need to change to make it work on a continuing basis. For instance, the movie
12 Monkeys postulated that time was immutable and a time traveler could only participate in the past that already existed, but the TV series took the approach that changing history was difficult but possible, since that was more feasible for long-term storytelling. And to stick with the simian theme, the '70s
Planet of the Apes TV series replaced the movie's mute, feral humans with fully intelligent, civilized humans who simply lived under ape oppression, so that the episodes could focus mainly on human guest characters with only a few ape characters needed, to save on the makeup budget.
Or sometimes a TV series is a loose sequel to a movie, a continuation in the same universe or one similar to it.
Starman was about the alien from the movie coming back 15 years later to connect with the son he conceived in the movie, although it bumped the movie's events back a dozen or so years so that it could be set in the present.
Alien Nation was a more faithful sequel to the movie (albeit with a few tweaks) and just told stories about the world and characters that the movie established but barely explored. Ditto
Stargate SG-1. I could imagine them doing something similar here, though I don't recall if the movie's worldbuilding laid interesting enough foundations to build on.
Now I'm wondering how many people died during TOS and what percentage of those people were security, and realistically, why anyone would want to serve under Kirk if the body count was as high as redshirt memes might suggest.
Here ya go:
https://www.ex-astris-scientia.org/database/redshirt_deaths.htm
A total of 56 fatalities across the second pilot, TOS, and TAS (which had no onscreen deaths except in "The Slaver Weapon"). I'd say that was 13% of the crew, but presumably each fatality was replaced to keep the number at 430, so that'd make it more like 56/486 = 11.5%. Although the bulk of the deaths are in only a few episodes -- the only ones with more than two fatalities are "Where No Man," "The Man Trap," "The Galileo Seven," "The Changeling," "The Apple," "Obsession," and "That Which Survives."
So seasons 1-2 both had 20-some deaths per season, season 3 had 10, and TAS had 0. So it seems Kirk got better at keeping his crew alive as time went on.