Let me preface this by saying I'm a financial planner, not a physicist and most of my physics knowledge comes from a combination of Art Bell and the science channel. But I believe strongly in the butterfly effect. Look at Gillian Taylor. Yes, she may be a minor player in time. But suppose six months after she left she was meant to cause a car accident killing the man responsible (or even his mother before he was born). Or even something as small as Kirk delaying the double dumbass a few seconds.
So, do you believe that the times make the man, or the man makes the time? In other words, do you feel that World events are dictated by the lives of specific individuals, or that specific individuals lives are dictated by World conditions that they live in? Why does it have to be exclusively one or the other? I believe that reality is a little bit of both.
Consider the US Revolution, for example. The American Colonies were under so much pressure from England that revolution was going to happen. If Washington, Jefferson, Franklin, etc... were not there, I believe someone else would have stepped in and taken their place in history. The times were ripe for change. Those dominoes were going to fall.
Now, how those dominoes fell may have been different if those people were not there. General Washington led his troops and made tactical decisions. Another general may have made different choices. Different battles may have been fought. The British may have put down the rebellion. It's just as likely that the Revolution would have proceeded without the historical figures we know.
So, while specific events may indeed be different, the overall generalities of history may be close enough to our reality. Gillian Taylor may have killed/saved the life of somebody instrumental in starting or preventing the Eugenics Wars. On the other hand, that would only be one individual. Khan wasn't solely responsible for the Eugenics Wars. No one individual has that much influence.
Now, to invoke Godwin's law and bring this argument around to the Nazi state, for example. It seems like a common time-travel story involves going back in time and killing Hitler, as if he was exclusively responsible for the Nazi state and WWII. He wasn't. He had all kinds of fellow henchmen to assist him with his twisted schemes. Had Hitler not been present, would someone else have been influenced by Himmler, Goring or Goebbels? They may have not enacted their ideas in the height of war, but, perhaps, their genocidal desires would still have been acted on. Perhaps the killing of Hitler would have lead those three laying the groundwork for the Eugenics Wars. Meanwhile, Hitler's life or death would have had no influence on the militarism of Japan. Perhaps WWII would have still happened, but the Allies and Axis totally different in structure.