Ah, the but the whole point behind this particular episode is not the plot, but the allegory of absolute power corrupting.
Or, imagine "The City On The Edge Of Forever" written as a proper time travel story that does not invoke a paradox. The very existence of that glaring logical flaw prevents me from becoming emotionally invested in the story. Put simply, paradoxes cannot happen. The only way to explain TCOTEOF is to use a multiverse—alternate histories. In this scenario, the Enterprise would not have "vanished" and left the landing party stranded. That would eliminate the the most compelling reason to venture into the past, aside from recovering McCoy. (For that matter, why couldn't they have simply asked the Guardian to pluck McCoy out of the past and return him.) Thus, Spock's "millions would die who did not die 'before'" is also irrelevant. In the alternate history, they'd die just the same.
The only thing McCoy did was "turn the steering wheel" up an alternate path. I'd assume the Guardian is so multiply connected that it could recover the travelers even from the alternate timeline. (By the way, the episode never tells us how the trio made their return. Did they signal the Guardian some way, mission accomplished? Or was simply meeting up with McCoy sufficient? If so, then intercepting McCoy on the sidewalk might have been the cue to return them all, leaving Keeler to step in front of the truck, but without Kirk and company to see it.)
In short, Kirk was under no pressure to "correct" history. But staying with Keeler would mean abandoning his command—and numerous other stories have shown which way that contest would go. (I believe the "blonde lab technician" whom Kirk "almost married" was Carol Marcus.) Any number of reasons might be worked out why Kirk couldn't simply take Keeler with him to the future.
There is a proper way to write TCOTEOF without invoking paradoxes.
Trek has used too many different, incompatible versions of time travel. The one I like is the Prophets, as non-linear beings who can see that time happens everywhere all at once and use that to 'intervene' in their own interests.
Most time travel stories in Trek are not that, they are Many Worlds Theory where we, the audience, jump tracks (sometimes with a handful of characters) and it is portrayed as, 'Oh no, time has been overwritten,' when the original timeline is carrying on just fine. It's so messy, it isn't even clear if any of the Trek shows are all in the same reality any more. The stakes feel lower but as in Mirror Mirror, the presence of the heroes can make a difference even in a Many Worlds scenario. Their mere presence 'creates' a reality only in the respect that they have turned up in the reality where they always turned up.
So CotEoF doesn't lose its emotional resonance for me but it becomes a far more selfish story about 3 men getting back home at the expense of a woman. Obviously, as viewers, we know that these versions of Kirk, Spock, and McCoy will go on to save planets, including Earth, but from our perspective at this moment, their motives are entirely selfish. The reality in which only McCoy shows up and Edith lived, carries on as normal, as does the reality where Kirk, Spock, and McCoy decide to save her and stay, the reality where they bring her to the future etc.
In their defence, it's pretty clear that none of the crew seem to understand temporal mechanics, so maybe their motives aren't subjectively selfish, even if their actions are self serving. I suppose one could also argue that they are doing it for Scotty, Uhura, and the security team, who are stranded but also have an escape route.
A better option would have been to jump back to the point where McCoy arrived on the planet and just stun him. Or maybe switch the Guardian off and on again.
What makes absolutely no sense in any universe is the Temporal Police. Time travellers exist, so timelines affected by time travellers exist. It seems futile to employ people to create timelines where time travellers interfere with other time travellers. Year of Hell is a weird example. Firstly, it's starts off in a different timeline because nobody remembers Kes' warning from Cause and Effect, which she couldn't give because she isn't here. Secondly, it ends in a different timeline to where it starts, since nothing the characters did in the preceding episodes has any impact on their decision to go around, not even Kes' warning. So people are right to question which reality Picard is set in but it certainly isn't the same one from the Cage.
That might just change history a little.
