well, I don't know about the writers but when it comes to what Alice Eve thinks that Carol should do, everything I've read her saying is a variation of this more recent comment:
Eve also spoke about her character’s lack of romantic times with James T. Kirk and it also appears that Eve is on the list to appear in the next Star Trek film playing Carol. “Obvious I would like to have a romance with Kirk. I think being pregnant in space would also be interesting and raising a child in space, also be worth investigating. And perhaps, nobody knows who’s child it is,”
the best part is"nobody knows who’s child it is"
star trek into soap opera
tbh, if Kirk had to have a romantic interest I wish they kept Gaila then. She was alien, cute, funny and even if she turned a bit soap opera in the end at least it was coherent with her character. It would have been funny for Kirk to fall for a girl that was a "manizer"