Having Kirk's story end with him deciding to be there for his child instead of just staying in Starfleet for the rest of his life could be a powerful ending, assuming they were planning to go that route.
It wasn't planned as the end of kelvin trek though, and they would never make Kirk leave starfleet to be a father, especially not when they'd end the movie with a cliffhanger with the intention to get a fourth movie and more. JJ once said (after stid) that they would never make Kirk settle down.
It's kind of obvious to me, while listening to that podcast, they wanted him and Carol to have issues so she'd leave to raise her son alone (assuming she wouldn't lose the baby when they apparently make her almost die), just like it happened in prime.
It's another reality so it's forced either way because they are literally paired together just because they had a thing in prime.
That would have been a fun twist, but I think having Kirk deal with becoming a father would be more interesting development for his character. A huge part of his story is that he never knew his father, and Pike challenged him to do better.
Tbh, I don't think that Kirk getting one of his crew members pregnant is a necessary or interesting character development. The guy needs to resolve his issues first and understand his role as a captain, and grow as one because he lacks experience as he got a promotion too fast and never had to truly earn this role like other captains (including Kirk prime) do. He also has many dynamics already; if you want to add yet another relationship for him, at the risk of truly making it an unbalanced Kirk show (
at least if Mccoy was the one dating Carol, it would also be an attempt to give the crew a life outside of Kirk, which is very important imo), you may want to develop it a bit first before jumping to break ups and babies. I'm not opposed to Kirk having a love interest but 1) no to them making it the Kirk show, again 2) quality >>> quantity. He has so many dynamics that need development. It is wise for them to focus on his developing bond with the crew as his surrogate family first, then think about exploring other things later.
Besides, even when it comes to a 'becoming a father' storyline, Kirk isn't, necessarily, the most interesting, powerful choice - or the one with more potential or fitting to this trek.
I, for one, find Sulu's subplot from Beyond interesting, however subtle it was.
And I mean, Kirk never met his father and I get it but...Spock is a half vulcan man who had a conflicting relationship with his vulcan father since he was a kid, and he experienced the trauma of believing his own father didn't even
accept him and didn't love him and his mother. Talk about having daddy issues! He spent most of his young life as someone who was discriminated because he's a mixed kid. He'd likely want to be there for his kids and do better than his father, but he may also feel conflicted about having kids because he is scared his own kids would endure his same anguish and discrimination. There is, also, the question about how the vulcan survivors would consider his kids after the vulcan diaspora. That's a lot of material to work with.
If you
absolutely need a pregnancy storyline (that is, tbh, kind of problematic by itself - and tricky for the female character - because they are on a spaceship) it would make more sense and be more interesting and new with
Spock than Kirk,
anyway. For one, unlike Kirk, Spock does
have an established relationship since the first movie; Uhura getting pregnant
by choice of both would feel a tad more natural for a sequel. Besides, it would also be more symbolic and powerful to have a new character linked to the iconic crew who
literally exists only in this trek. A character who would also be the son/daughter of an interracial/interspecies couple, versus being the human kid of a cis white human couple. I mean, no offense to humans but they aren't exactly groundbreaking and original in a thing like trek. They need to try to do better.
The storyline they had in mind for Kirk and Carol in that pitch is not only unoriginal because it's a repeat of what happened in prime, it would also make them both look like irresponsible teenagers because they are both humans and it's not plausible that birth control isn't a thing in their reality, especially in Starfleet. With Spock, you could at least 'explain' an unpredictable pregnancy using the fact he's half vulcan as an excuse (but still I'd find it a bit lame. They aren't in middle age! ), but here you have Kirk secretly sleeping with one of his crew
and getting her pregnant. They borrowed a storyline from TWOK, again, but made it even..
worse. In the metoo era it wouldn't look pretty to general audiences, tbh, especially if used as a set up to get rid of the female character in the next movie.
And I mean, I'm
sure a lot of the fans who harpy on Spock's relationship with Uhura and call it 'unprofessional' since 2009 would magically give Kirk a pass - in spite of him having a role on the ship that would make him sleeping with a subordinate and getting her pregnant much, much worse (he literally is everyone's boss) -, because some of the old trek fans are predictable like that when it comes to being selective with their outrage, but the audience who already called stid sexist for that one Carol's underwear scene would have a nervous breakdown about that kind of storyline. Especially after they had already mentioned Kirk having a fling with Chapel
too previously,
which resulted in her leaving the ship for his fault.
Maybe Paramount rejected Miller's pitch because it would execerbate issues stid had/was criticized for, including them using Khan again. Maybe the studio wanted a new direction but is apparently struggling to find writers who are truly inspired to do more with this trek instead of constantly borrowing stuff from tos. Even with Tarantino they had no luck because he doesn't even get it's another reality. And the new director they are in talks with apparently has new ideas, but he wants to ignore the kelvin trek cast. It's a pity.