Why do colleges run football teams?

Over at Free Exchange Isaac Bickerstaff poses a good question:

…why are America’s institutions of higher learning also operating
semi-professional sports franchises?  Especially since overall, the
athletics department is a money-losing proposition for most schools. 
They also bring down the value of the university’s core "product", as
schools offer places and often lavish scholarships to academically
unqualified student athletes.

The evidence is mixed, but some papers find a connection between athletic achievement and student quality, or athletic achievement and alumni donations.  I suspect the donor connection is the key, but we also must ask what exactly colleges and universities seek to maximize. 

Under one view, there is some local market power, a surplus from tuition and endowments, fairly passive boards, and a faculty-driven governance structure which gives Presidents considerable discretion over non-instructional projects.  If I were a University President, I would spend money on the library, a very good music school, a concert hall, and — if they would abolish the NCAA and the zone defense — a basketball team.  Basketball is The Queen of Sports, and what better way to entertain local bigwigs and receive favors in return?