why not?
I always thought they could make a spin-off set in the future where some of the next generation characters are linked to the ones we know.
You could have Spock/Uhura' son or daughter as either the captain or the ship's doctor (imagine a series that is more focused on the perspective from sickbay rather than the bridge all the time?). You have Sulu's daughter too. Leave the possibility of the old characters making a cameo, but don't (e.g., Discovery) make their whole arc all about them being offspring of x character because it's boring. In fact, it would be great if you get only some clues about the connection and then it's revealed only later. And yes, make them totally new people and not really a 'copy' of the 'roles' the old characters have in fans mind.
actually, speaking about 'new people', a friend of mine asked me if S/U, as well as the other characters of the kelvin timeline, can have kids in this reality in spite of not having them in tos. My friend was like 'it seems like only those who exist in tos can exist in the kelvin timeline too' and that got me thinking about this a lot because it's a fascinating concept, actually. I didn't want to open a thread because I don't think it's a topic many people would care about but I surely thought about it.
Truth is, from a realistic (as realistic as you can be in sci-fi that still has fantasy elements) if alternate (quantum) realities exist, there is no reason why a person must be born in every possible reality. The concept is that destiny doesn't exist and everything is supposed to morph and change (across realities) according to simple events that may happen or not happen.. so yeah, if your parents never met or they broke up before conceiving you, I'm sorry but you may not exist in that parallel reality. But does that really matter as long as you exist in your own? Your different realities counterparts would be different people anyway and you aren't living their life, and them living their life or not doesn't change yours. This could be a good pretext for a bit of character conflict (e.g., them discovering that in another reality they were never born)
Point is, the idea that all the characters we saw in tos must exist in aos too and viceversa, those that don't exist in tos can't exist in aos, is a tad forced and silly and it really is more a limit that writers implicly and naively put on their narrative (because, of course, we gotta get a Spock, a Uhura, a Kirk etc etc) than the most logical idea. And yes, it kind of seems a bit like even with Sulu in Beyond there is no real 'new' if it comes across as if he can have a baby girl only because he had one in tos too. People even automatically call her Demora, in spite of us not really nothing if she's exactly her or if she CAN even be her (if her other parent isn't the same it was in tos, as Pegg had apparently implied that Sulu dates men only in this reality, then she can't be ). Was that a homage from the writers' perspective (giving him a daughter instead of a son), or is it truly a sign, again, of this almost subconscious limit the writers put on themselves that prevents them to truly imagine this as another reality full of new possibilities? The latter is a big depressing for me, and honestly a wasted potential.
tl dr: an issue this timeline may have had from the start is that they tell us it's an alternate reality but they don't exactly embrace the concept fully because they don't, in a way, let this trek BE an alternate reality where things are ruled by casuality rather than destiny, or fate concepts, that may not truly fit with the presuption trek has to be inspired more by visionary science than pure fantasy genre.