There are categories in copyright law - you have to check whether your name has already been taken by something else in the category. For instance, a computer game company I worked for wanted to name a game "Vortex." Of course a copyright search turned up a ton of stuff - a nightclub by that name, a potential movie, a motorcycle company, etc.
I'm sure there was a rock band by that name because there's a rock band by any name you can imagine.

Only the movie was a problem because it was in the same copyright category as computer games (being media entertainment).
Naming a rock band T'Pau might be okay but try giving that name to a computer game, even one that has nothing to do with Star Trek or that character, and you're in trouble. (This is all iirc - it's been a long time since I've done a copyright search like that.)
I don't see why a late 24th or early 25th century show couldn't be done. Costs for effects and film editing have dropped dramatically; even amateurs can make relatively slick films with off-the-shelf equipment. Why couldn't CBS let a bunch of obsessed fans make a show and let it run on a cable channel, such as ScyFy? They could allot a fairly modest budget, and if it's run by the right kind of devoted fans (who are plentiful and not interested in being well-compensated), it could be very good. It wouldn't make much money, but it would probably turn a profit and give immense satisfaction to die-hard fans. Now that TV has room for such niche shows, why not?
Haven't some of the independent fan creations shown that it's possible? Obviously it'd have to be of a higher quality and be official and all that, but I think it'd be doable without breaking the bank or interfering with the successful new movies.
The only tricky part would be getting quality actors, but I bet there are many good ones I'm Hollywood who are between jobs.
Can someone explain to me why this isn't being considered or it's a bad idea?
Because nothing you mentioned is a factor that would motivate CBS to do a 24th/25th C show. Here's the problem:
CBS wouldn't want to do a
Star Trek show at all. They are making tons of money just doing police procedurals. Have you taken a look a their lineup? The Dominion doesn't have that many clones!

But their audience loves that shit - CBS is doing great in the ratings, while its network competitors are floundering to varying degrees.
The market sending a clear message to keep doing exactly what they are doing, with no variations, and they are complying. Why wouldn't they? The people who make decisions keep their jobs only if the money keeps flowing in. They're not going to risk their jobs over
Star Trek!
Nobody is doing space opera, not even the so-called "science fiction channel." (Unless you count
SG:U, which is too depressing to think about.) Why would CBS want to do space opera? It doesn't do sci fi of any sort, not even one of those cop shows with sci fi window dressing.
It could produce
Star Trek for one of its channels other than CBS, but what would that be? CW? Showtime? They're both wrong for
Star Trek.
So what could possibly motivate CBS to ignore the huge disincentives to making a
Star Trek series and do it anyway? Only the hope of making massive amounts of money. The track record of
Star Trek on TV does not scream "cash cow." Maybe
Trek XI doesn't either - movie success doesn't guarantee anything about TV success - but it's the one and only element that might grab CBS's attention for a brief millisecond before they go back to planning
CSI: Paducah.
If by some miracle, they do a
Star Trek series for Showtime (which is more likely than CBS or CW), then they'll cater to the Showtime subscribers. If they don't think they can interest Showtime subscribers in
Star Trek, it won't happen at all.
Yeah, like it would really fly having a show but not committing to which reality it takes place in? Trek fans would stand for that? They are critical and relentless.
The number of potential viewers who would notice whether a
Trek show on TV matches
Trek XI is not enough to cause a blip in the ratings. CBS would not bother making anything for the tiny number of people who care about stuff like that, much less bitch about it on BBSes like this one. They'd need a big audience, at least 10M, or they won't bother.
By any definition,
Star Trek "fans" are too few to bother making TV or movies for. In either case, you need to cater to a mass audience. We were just lucky that
Trek XI was pretty respectful of
Trek lore. Abrams could have had a big hit while thumbing his nose at all of us. He doesn't need
us; we need
him.
And if it is any consulation, it is likely that Abrams wouldn't actually direct the TV series.
I'd love to see him produce the TV series, but I doubt it's a priority for him. However, nobody is going to produce a TV series that doesn't at least have his blessing, because the money his movie made has now made him Mr.
Star Trek. In the Hollywood heirarchy, money is the only thing that counts.