I think Noel would have been difficult to write for. As portrayed she was every bit Kirk's equal intellect and gumption. She also was (as I gather) able to keep from being overwhelmed by his charms, even though she might have been willing to have a relationship on her own terms. There was an awful lot going on with her and relegating her to a secondary role would have been extremely difficult and giving her more screen time would have meant less for someone else. Too bad, really. That combination of brains, beauty and courage still packs a knockout punch to this day for me!
I know this is sacrilege, but if screen time is the issue, I'd part with McCoy. I think Noel would have made a better foil for Kirk and Spock. She could bring in everything McCoy did, as the emotion or "Id" part of the triad, and on top of that there would be implied sexual tension.
It was not a "law" of '60s television that caused female shipmates to be marginalized on Star Trek
. It was Gene Roddenberry's unexamined, automatic assumptions about the primacy of male characters, combined with his need to keep Majel Barrett in the dark as to NBC's real reason for rejecting her.
Other shows of the period had female co-stars who were fully involved in the plot and who often motivated the action. Star Trek
, much as we love it, was just unevolved in that area.