I don't think the concept of the project is the problem. I'm skeptical that an "Uncommons" project built around fair use could be workable, considering that the validity of a fair use claim is context-specific and no cross-wiki project (like Commons) is going to have an easy time managing that requirement.
The problem is the behavior of a certain core set of Commons admins; time and time and time again we have it reported here, we see it on Commons. While not lawyers, they attempt to be extraordinarily demanding when it comes to "legal" accuracy. Far more than the actual WMF lawyers have required, incidentally.
It's not surprising that the locus of the dispute often revolves around community members who have been banned on other projects but reached positions of authority on Commons. Perhaps Commons social structures haven't evolved enough to deal with people who are both productive and deeply disruptive, and who are not uncivil but contribute to a toxic environment.