In the real world, though, athletics keep at-risk kids in school and trying to get grades because they want to play and need to make satisfactory progress in order to do so. Athletics have helped a ton of kids grow into prosperous adults because it kept them invested in their educations until they realized that it's what they needed to do anyway.
To that I say:
1) Plenty of poor kids do find ways to participate in school sports. Let's not throw that baby out with the bathwater.
2) Where this is not possible, it would be better to find ways to make it possible than to get rid of something good for everyone.
If you want to have public sports programs, that's fine. It has nothing to do with school, should be an entirely separate pool of money, and IMO, should be entirely self-funded.