I don't think knowing about science had much to do with the success of Star Trek. You're probably right about the professional science fiction writers, though. Did they stop using professional sf writers for the third season?

In general, does having professional science fiction writers reliably contribute to the success of movies?

A data point which may not point in any particular direction: I was delighted by Gattaca and The Truman Show-- even if I had specific nitpicks with them [1] because they seemed like Golden Age [2] science fiction. When composing this reply, I found that they were both written by Andrew Niccol, and I don't think a professional science fiction writer could have done better. Gattaca did badly (though it got critical acclaim), The Truman Show did well.

[1] It was actually at least as irresponsible as it was heroic for the main character in Gattaca to sneak into a space project he was medically unfit for.

I don't think Truman's fans would have dropped him so easily. And I would rather have seen a movie with Truman's story compressed into the first 15 minutes, and the main part of the movie being about his learning to live in the larger world.

[2] I think the specific Golden Age quality I was seeing was using stories to explore single clear ideas.