Of course, but that's not the point. I'm not saying he didn't have game, I'm saying he didn't let it distract him from his duty in the middle of an active mission. Well, he somewhat did with fake Ruth, and he definitely did with Edith Keeler, but Edith was anything but a casual fling, and from Kirk's reaction to Ruth, it seems she wasn't either. The point is, given the urgency of the mission to find the Soul of Alar, and given the extreme and constant hazards of the mad planet, it's perfectly in character for Kirk to table any romantic interest in Lara and stay focused on the mission. If they'd run into each other after the mission, when there wasn't anything more important at stake, they might very well have ended up making some "green memories."
Again, he was only using Lenore to investigate her father. With Miri, he sweet-talked her because he needed her help and allegiance for the sake of the mission, and the episode was written in a time when it was taken for granted that the way to get on a woman's good side was with flirtation and flattery. In both cases, it was in service to other goals that had nothing to do with his hormones. With Areel, she was an old flame from his past, so the relationship was already there beforehand.
And most importantly, none of them were his direct subordinates. He was Rand's superior officer, so romancing her would've been sexual harassment. It would've been a gross abuse of authority and totally unconscionable. So it's a completely, profoundly different situation from the other cases. Granted, workplace harassment was seen as normal and routine in the '60s, and there was certainly plenty of it going on in Gene Roddenberry's office, but even at the time, they knew it would've been incompatible with military discipline for a captain to seduce someone under his direct command. (This is why Kirk was so uncomfortable with Helen Noel in "Dagger of the Mind." A deleted scene revealed that he'd only danced with her at the Christmas party because he'd thought she was a visiting civilian. On learning that she was a member of his crew, he was mortified at the accidental breach of discipline.)
I just thought Kirk wasn't into Lara. People can be too assertive and she wouldn't take no for an answer. Which is one of the main things I remember from the episode (with a laugh).
The thing about Rand and Kirk is that I thought there was zero chemistry there. Kirk gave more of his charm to everyone else on board. Even Scotty and Spock garnered more smiles out of Kirk than Rand ever did. I know that Kirk said he wanted to be able to "date" Rand but I never felt that he really was infatuated with her as a person or that there was any unrequited love there. I thought Kirk's lament that he wanted to be able to date someone (not specifically Rand) but his first loyalty was to his ship and his command so a woman would get in the way.
Perhaps if Rand had been the yeoman instead of Noel or in Shore Leave maybe I could see them together.
Also I don't think the casting was right for such a role.Whitney appeared too smart to just be some infatuated young girl. I think she would have need to show more gumption or something to make her worthy of Kirk's love. Making coffee under difficult circumstances doesn't cut it for me. Perhaps if she'd replaced Helen Noel and managed a jail break...