In "Yesterday's Enterprise", how did the Enterprise-D's crew come to be together when obviously the history of each crew member was very different than in the "prime universe" up to that point?
It's true that the changes could have greatly affected each of the people who were there. But at least they gave it a minute of thought as to who should be there and who shouldn't. Worf and Troi were cut since it didn't make sense for them to be there, and Yar was put back. If the writers of the movie thought the same way, they probably would have eliminated Chekov. But they didn't really care if it made at least some sense, and to a certain degree we have to accept that writers are just going to put in what they want. All that really matters is that they maintain the illusion that it makes sense.