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.
They didn't put in "what they wanted". They put in the "Big 7" regulars from the TV show and the films.
Eliminating Chekov would have raised a terrible ruckus. There would have been throngs of fans saying "this is Star Trek; we would have created ways in our own minds by which Chekov could be part of the crew! That's what we have always done with canon."
And please don't tell me that it makes logical real-world sense that Wesley ended up as part of the "Yesterday's Enterprise" Enterprise-D crew, sitting in the chair next to Data. I'm okay with it, because it is only Star Trek (a fictional story), but it doesn't really make that much sense in reality. It's quite the coincidence.