I think an anthology format could work for Star Trek. After all what do you need?
A Bridge, well if you build a modular bridge as a set you can move the modules around to get a different format of bridge if you wanted, but there is no reason as to why multiple classes of ships could use the same bride. Same goes for the rest of the standing sets, Transporter Room, Corridors etc...
But if you're going to do a Trek-universe anthology series, what's the point of just doing various different starship crews? If you're only doing starship stories in a single era, you might as well just use the same cast week after week. There's so much else to explore if you really want to embrace the anthology format. Do something set aboard a starbase. Explore the civilian side of the Federation. Do a drama about WWIII, and follow it up with one about humanity in the wake of first contact, adjusting to the presence of the Vulcans. Show us the Romulans' exodus from Vulcan. Show us the life of Kahless, or a story from the brief war in "Errand of Mercy" from the Klingons' point of view. In short, do the sort of things the novels have been doing for the past decade or so.
I often thought, back in the '90s, that Paramount (who still owned and produced the series at the time) should do a regular series of Trek TV movies, maybe 4-8 per year, in that vein -- mingling ongoing/recurring series and single standalones set all over the Trek universe in many different eras. It would've been a good middle ground between a weekly series, where you get a lot of installments per year but only limited budget and time to do each one, and feature films, where you have the money and time to make it more elaborate but with only very infrequent installments.
Unfortunately, the idea of ongoing series of TV movies, which was popular in the '80s and early '90s with things like the Columbo
and Perry Mason
revivals, seemed to start fading away about halfway through the '90s for some reason. The Universal Action Pack tried a movie-wheel format for one season in '94, but then switched to doing just a couple of weekly hourlong shows. And these days original TV movies are pretty much extinct, except for cheap productions on some cable channels. The idea of an ongoing franchise of TV movies in a single continuity is pretty much extinct in the US -- although in the UK they still have things like Sherlock
and Inspector Lewis
and so forth.