I think it depends on the school how important this is, I kind of doubt Harvard needs to raise awareness. But there are other benefits of sports that will also

I think it depends on the school how important this is, I kind of doubt Harvard needs to raise awareness. But there are other benefits of sports that will also depend on the particular school. One factor that comes to mind is location- Notre Dame is in the middle of damn nowhere, if they did not have the appeal of the football team I think they would have a harder time attracting students to actually go there (regardless of name recognition). It also will probably depend on how much the rich alums care about sports, so again for a school like Notre Dame that has always been big on sports and is also very big on legacies and promoting alum community and what not, it makes sense. To be honest I don't see why it matters much for today's Harvard though, at least none of the benefits I can think of really line up. Plus Harvard can never attract the truly best athletes because no Ivy scholarships/the generally lower level of Ivy competition in most sports. Maybe they just care about being better than Yale.