I think the Spock/Kirk fanfic developed because a lot of female fans (including me) had the hots for Spock, and didn't want him going into pon farr with some random girl back home on Vulcan, or with Nurse Chapel, or some Romulan bimbo. I once wrote a fanfic in which a half-Vulcan half-Betazoid female joins the crew of the Enterprise, and goes into pon farr - and the only person she can safely mate with is a half-Klingon half-human. (She was a total Mary Sue, of course.)
Re: Yes ...