I don't see why schools like UK and UNC can't just offer a major called "basketball," "football," whatever. Give 60 credits for playing basketball, require 30 credits on other sport-related coursework, and require 30 credits in all the other stuff any other student takes. The free market will value this degree as they deem appropriate.
How many credits does a bachelor of music in piano student at Julliard take in math, science, foreign language, business? From what I can tell based on perusing their website, the answer is very few. As a result, Julliard students probably don't often get hired as accountants or to work in chemistry labs. So it goes.