My small private school runs football largely because it is expected. We don't sell out (we even discussed eliminating ticket prices entirely). And, yes, there are alumni who donate to the program. But plenty of alumni at basketball-centered schools have connections to their schools w/o football. See Seton Hall, Xavier, GWU, Gonzaga, etc.

If it weren't for the NCAA subsidy, we'd drop almost all our sports. And that's the case for most DII and DIII schools.