But that's what they did, isn't it?
Episodes tended to focus on a specific set of character. The big cast actually worked for me and I liked the episodes that involved all of them just as much as those that focused on one or two characters.
A large cast of characters works for me. It makes the world feel bigger and more complex. I prefer that over having the same 3 guys on screen all the time.
Shows like DS9 or even Lost are good examples of that. Tons of recurring supporting characters and also a large number of "main" characters that give the shows consistency.
I'm not saying the cast should've been smaller, I was fine with the size, especially for a show projected to go seven years. My peeve is cramming characters into episodes they really didn't fit in just to give them screen time. I don't know if they thought the audience would forget that LaForge or Troi or Riker or Crusher exist if they didn't make an appearance in every episode?