Agreed on these points!
I don't think there were too many characters, but, one of the drawbacks of having a larger cast was the fact that it became very difficult to highlight all the characters equally, although it was clear that the writers tried to do that. This resulted in a lot of character-oriented loose ends at the end of the seventh season that were completely unaddressed by the movies.
The strength of TOS was its ensemble cast, although a handful of the characters were featured more prominently than others. TNG, I think, had a similar strength on TV, but that strength was very much downplayed in the films. I think that First Contact was probably the only film that, by distributing the main characters between two plot scenarios, achieved some level of character equality.