In 1987 after four successful Star Trek movies why didn't Paramount produce a series based on the original crew? Why did they opt to create a TV show based on a new crew 70 years after the movies were set? It seems pretty dumb to me considering they were making so much money on those movies.
If I understand correctly, once Paramount made Roddenberry executive producer, it was Gene's own idea to set the show that far in the future, because he wanted to get away from TOS and the films as much as possible, because he didn't like where they were going and wanted a clean slate, which to him meant setting the show at a point in time where nothing from the past would interfere with it.
He was able to get away with that because this was the first time Trek had ever come back to the small screen, and fans would have been fine with literally anything that was shown to them. They were just happy to get a new Star Trek television series since the original. And between that and the show being syndicated, it was able to survive even though it probably would have been cancelled after the first or second season had it been shown on a network.
Of course, nothing like that would fly today.