And remember that TOS was in the 60s, when you could get sex like turning on hot water. Compared to James Bond of that era, Kirk is a celibate priest.
You could get sex in the 60s, you just couldn't show it or refer to it even indirectly on network TV.
By present-day standards, the limits on what could be shown back then were positively draconian. 'No open-mouthed kisses' doesn't even begin to cover it. You could bare the breast
almost down to the nipple, but never EVER show the underside, and the navel was completely totally irrevocably off-limits. And anything other than a "completely normal" heterosexual relationship was never mentioned or implied E-VER.
It wasn't really a lot past when a couple could only be shown in bed if they were married, had separate beds AND one of them had at least one foot on the floor.
Also noting that the network, at one point, pushed very hard for the Enterprise to have an all-male crew, because a mixed crew implied a lot of "fooling around". No one there seemed to think of the implications of a same-sex crew on a long-duration mission at all.
Other factors to bear in mind.
First, there was GR's take on the character. Time and again, Kirk was noted as being 'married to the Enterprise' and, whilst he enjoyed the company of women, the Big E always came first. Think he even said so himself a time or three.
Second, 60's TV show thinking. If Kirk (or any other male lead) was in a steady relationship, there was the fear that this would impact his female fanbase. There would also be speculation on their "fooling around", which would also impact the 'Family Values' fanbase - who would also probably demand that they be decently married. Which, if done, would hit the female fanbase even harder and, if NOT done, would get the 'Family Values' types and the Bible Belt threatening to boycott whatever. Better to play it safe and just not go there.
No foolin', that is pretty much how the network / studio types would have been thinking back then.