FWIW, I recall an interview with Tarantino on YouTube somewhere in which Trek came up, and he was asked to name one of his favourite episodes.
To my surprise he named Yesterdays enterprise. He genuinely seemed to love it and remembered a lot of details about the plot. The other he mentioned is city on the edge of forever.
So while many might react to the idea of an R rated Tarantino Trek film negatively, I’d be quietly optimistic that he has good taste in Trek and would have a good core of a premise and story. I suspect he’d also handle the characters well, knowing how to balance campiness, seriousness and comedy.
EDIT: Found the interview: https://www.youtube.com/watch?v=WyD7CFnFH3A
It’s from 2015. Go to 3.47 for the relevant section. Interestingly, rewatching it, the prompt of the conversation was “what Star Wars movie would you like to do” and Tarantino responds with he’d rather do a Trek film.
And to further my point, he’s main point is that so many good episodes from Trek, especially the original series, could be made into movies.
City on the Edge of Forever is the best TOS episode in my opinion, and surpasses 90% or more of all Star Trek across all the series.
It’s good to know he knows his Star Trek. But I still wouldn’t want a Tarantino Trek movie — unless, of course, Avery Brooks reprises his role and recites Ezekiel 25:17 and has a phaser with Bad Motherfucker etched on it. That’s a Trek movie I’d watch.