I've never felt the need to 'edit out the silly' from this film. I've long described it as good science fiction, and bad Star Trek. But the story has nothing to do with why I describe it that way.
I have two primary complaints about this film:
1) The editing is incessant, and choppy. There is so much effort in giving the rest of the cast "their moment" that it interrupts the flow of the storytelling. The Star Trek I watched as a child, and in previous films, progressed much more smoothly. Just one example of what I mean is the scene where the Enterprise arrives at Nimbus Three, and they begin their plans for raiding the settlement. Between "giving Uhura her moment" and putting each character front and center for line delivery, there are nine cuts in a two/three minute scene. The same scene would be much more economical with Uhura's line as a voiceover while Kirk and Spock are talking, resulting in a maximun of four cuts.
2) Bran Ferren and Associates annoying habit of having a prestige effect being something minor, while the big effect/s at the climax being done with baling wire and spit. A better set of SFX, preferably by a more reputable effects house, would do wonders for how this film is perceived.
The humorous moments are usually staged to make the studio heads happy, rather than the target audience, and that could be done better, but I don't think any of them need removed. The above is what frustrates me about what could have been a great movie.