The worst offenders for "love interest of the week" in my opinion were the nonsense between Spock and Droxine in "The Cloud Minders" and McCoy/Natira in "For the World is Hollow and I Have Touched the Sky."
I hate to bring up this episode, but I can't think of a worse 'love interest of the week' than whoever Jadzia wants to throw her life away for in "Meridian" (forgot the guy's name). It was much more convincing when she wanted to leave her whole life behind to be with someone knowing there would be serious dangers and consequences involved in "Re-Joined".
As for "The City on the Edge of Forever", I disagree that how quickly it happens makes the romance in that episodes unconvincing. I think they did as good a job as they possibly could doing that within the constraints of a 45 minute television episode.
And I don't know how anyone could not find the ending powerful, with someone having to let this woman he adores die when he knows he could have saved her. I was charmed by Keeler's kindness and idealism, so it was easy for me to understand why Kirk would adore her for that too.