As for sports being part of the college experience, I don't disagree with you that they are right now, but I don't see why that would have to be the case, since it certainly didn't use to be the case historically and still isn't the case in many parts of the world. From my perspective, they're so far removed from the actual purpose of universities that they've essentially marginalized the actual point of them for many schools, and the idea that they're integral to the experience is a sign of how much they've failed at their actual goal.
I think it tends to be in the Anglosphere at least. I won't really argue for the big college football etc. programs which has been an ongoing debate in the US for decades for Top 10 schools and related. James Michener wrote a book in the 70s or so. But athletic activities in various more or less organized forms are pretty established at many US schools and eliminating them would bring a pretty wide revolt (and not just talking about football).