You are right, she is still alive, but she might as well be dead. She was just there giving birth. Even in the deleted young Kirk scene, they rather introduced a stepfather than use her again. We still hear his voice though, while young Kirk is driving the car.
Well the stepfather/uncle is a "bad guy". So I'd rather Winona wasn't placed in thast role. Though I would have liked to have seen Winona in additional scenes, but I would prefer them to be scenes that advanced Kirk's character.
And I haven't seen Beyond yet. Maybe Jaylah's race joins the Federation or is already a member? She could join the ship, if they wanted. With the track record of these writers though, I doubt it will come to this.
Very few of us have seen the film yet. But it seems unlikely that she'd become a member of Starfleet on the spot. Now if the next film is set four years later, then she could join as a newly fledged cadet.
These writers, Pegg and Jung, have never written Star Trek before. So there is no track record. No idea what the previous writers had in mind for Carol, Rand or Chapel. They didn't get the job.
The point was also that seemingly only one female character, Uhura, is allowed to appear in more than one movie. They didn't introduce more female characters right from the start, for example Chapel and Rand. They also kept Pike around for longer, old Spock was in two. Keenser is apparently also worth more keeping around than Carol. Even the security officer Hendorff has a place in ST09, STID and because a movie seemingly really can't work without him, he will also appear in Beyond. But finding a place for Carol on the ship, she just joined in STID? No, that would be too much estrogen.
"Seemingly" is a pretty big word with a lot of room for supposition, assumption and guess work. Not always the best course.
Unfortunately, Chapel and Rand aren't seen as part of core group of characters. Would I have like them to play a larger part in these films? As a fan, of course I would. I would also have liked them to play bigger parts in the original fims. And as tragic as Anton's passing is, I hope they can possibly fill Chekov's spot with a female character. My choice would be Janice Rand, since she is an established character in the mythos. I'd also like to see Chapel on board as biologist. Rather than as a nurse or doctor.
Pike was kept to be killed. Is Hendorff in the new film? Thought he was killed in STID. Aren't there other female characters (abet in minor roles) that carried over from 09 to STID? And in addition to Jaylah, there is the Starfleet Commander role play by a woman. So there is some representation beyond the main cast.
As a whole Trek record of adding new characters to established ensembles is pretty weak
Decker and Ilia were basically killed off.
David was killed off.
Saavivk was shipped off to parts unknown.
Valaris was a bad guy.
Pulaski shipped off to parts unknown
The success stories seem to be Chekov and Guinan.