And what exactly was wrong with Alice Eve's changing scene? Sure it was a bit gratuitous but she certainly looked good in it and I didn't feel that it took anything away from the movie, even if it didn't add anything either.
I think you nailed it already. It didn't add anything nor take anything away so it's just pointless. Plus it doesn't really do anything for her character since JJ states it's just there for Kirk to have a moment at her expense. The only other thing she brings to the story is that she has daddy issues, because that trope hasn't already been done to death at this point in this new take of Star Trek.
But in all honesty, this pointless scene alone is not what bothers me. It's how JJ Abrams honestly believes he's made an even trade off with that one shot of Kirk earlier in the film. I'm sorry, but JJ is either delusional or thinks that women only have 1/3 value as characters compared to the male characters.