I don't mind the strong sports culture. College football has an immense history dating back to the late 1800s as an organized national collegiate activity. I'm a fan and I enjoy the history and pageantry of the sport. Athletic departments are self-funded by donations, TV rights, ticket sales, and merchandise, and they take no money that would otherwise be allocated to academics. They also can increase the brand of a university, as you pointed out.
I take issue with a couple things: First is that unpaid 'workers' are responsible for driving an industry now worth billions of dollars. Second is that some scholarship athletes are admitted to schools they have no business attending on academic merit, and end up in essentially remedial education. This is true even at prestigious schools with high-level academics.