I think you're right, if they'd tried to feature everyone every week. It might have worked if they'd gone for more of an ensemble approach, like you see in Deep Space nine, for example. In DS9 they had a large number of regulars, plus a pretty big list of recurring characters. But you didn't see everyone all the time, just whoever was needed for a particular story.
Phase II might have worked with this. You don't need Chapel every week. Heck, you could have gone a week without Decker or Xon with the right story. That would have saved some money, and maybe given the writers a chance to explore some characters they might not have otherwise.
Would that have worked on a ship, though? DS9 worked in part because it was set on a space station that functioned like a huge floating city. Sisko was the mayor: Odo was the police chief, and so on. Like any other community, there were the regular townspeople (Quark, Rom, Garak), plus frequent travelers who came and went as needed (Martok, Winn, Dukat, Cretak, Ross, Kassidy Yates, etc.). It wasn't necessary for the mayor or the city physician to play a huge role every week because each episode focused on a different aspect of the town and its history.
A starship is a different matter because most of the action happens on its bridge. You could write a story about something happens only in engineering or on the holodeck, but a reason would have to be given for the story's self-contained nature. After a TV series that revolved around two or three characters, it would have been difficult for the audience to accept a show that featured everyone, albeit across several episodes rather than all at once.
I think if Deep Space 9
had happened before TNG that it would have failed. The Next Generation
was a nice bridge between the two concepts and allowed fans to enjoy episodes that weren't centered only on the series lead character or characters.