Let's remember that while Kirk mucked about in the 20th century, he never created the sort of "uncontrolled" effects that would have significantly altered the future. He never prevented himself from being born, say, even though this would certainly be the consequence of removing a big war from the timeline. We're supposed to think that time in some mysterious way is self-healing, then, so that even the most blatant changes fail to create "ripple effects" of smaller changes.
On the other hand, McCoy did erase the entire UFP from existence by wandering around stoned in the 1930s. He apparently achieved that mainly through interacting with a "kingpin" figure, though; those might be rare and difficult to find, and simply killing a random bunch of, say, five thousand in any given era would not necessarily result in any sort of a noticeable change in history.
Edit: to answer any questions, Kirk and crew returned to their timeline because Spock used the exact same coordinates to get back.
But that would get them back to a timeline where there were no whales on Earth because nobody had traveled to the past to get any...
If OTOH Spock could guide them to a timeline where they had
gone to the past, why didn't he do that right away so that they could have skipped the actual, troublesome going-to-past bit?