A large state university with which I am familiar used to have a student organization called the State University Economics Association (not literally, but you get the idea). At some point they changed the name to the State Economics Association. The reason was that they could not have "University" in the name without following the university's requirements for student associations, and these requirements were sufficiently burdensome that the students did not want to deal with them. Paperwork was one thing, I remember, and there may have been other restrictions.
Recently, while walking through the campus of State University, I saw a number of notices for student organizations, many of which did not have "University" in the name. That tells me two things: students value the organizations themselves, but the resources that the university devotes to student organizations are largely wasted.
One response to the increasing cost of higher education is that universities should unbundle their services. Much as living in a university-owned dormitory is billed separately from tuition, other services, such as athletics or student organizations, could be available for a separate fee. Tuition would then be meant to cover only expenses directly related to the education itself (including some but not all of the overhead). Arnold Kling predicts that participation in social activities "would plummet. Students would find less costly ways to socialize." (He says some other interesting things about unbundling here.) I think that the goings on at State University support this point. Of course it is valuable for students to get together around various themes for fun, networking, or whatever else, but that does not mean that it is a good idea for the university to devote costly resources to such things. This is the kind of redefining of the university's role to which I referred in a previous post.