When you really dig down, the root of the problem with college basketball is the relationship with the NBA. The NCAA likes to talk about "student-athletes" while universities build palace-like arenas (and now practice facilities), pay coaches millions of dollars, and charge ticket-holders professional sport prices. The NCAA has not been able to decide if they are an amateur athletic league for students or a professional minor league, and they are trying to take the best (for them) of both.
My (unrealistic) proposal is to split the top tier of NCAA basketball (division 1-A) into a semiprofessional or professional minor league and a league of true student-athletes. Teams opting into the professional league might maintain some relationship to their schools, but would drop any pretense of academics; they would essentially be "basketball schools." They might implement some rules regarding player age or experience, but players would be paid like the professional athletes they are. Teams opting to remain amateur would operate more like the "lower" NCAA divisions, limiting or even eliminating athletic scholarships (and certainly banning athletic recruiting); players would be students who happen to enjoy the sport but are not on an athletic career path. With such a division, basketball players seeking a professional career would no longer be forced into pretending they want a college degree, the NBA could have a real "developmental league," and university administrators could spend more time and energy on improving the academic quality of their school.
The biggest problem I see with implementing such a system is that the schools that must be convinced are the schools with the most to lose, schools such as my alma maters of the University of Kentucky and Michigan State University, schools like North Carolina, Duke, Florida, UCLA, and Louisville. To ensure a smoother transition, and to make this proposal more palatable to these schools, they should be permitted to keep a substantial stake in their teams. For example, the "University of Kentucky Wildcats" might become the "Kentucky Wildcats," a minor league professional team owned and managed by the University of Kentucky. Or they might create the "University of Kentucky College of Basketball" (OK, School of Basketball in the College of Athletics).