I'd argue those jobs don't need one, either.
So someone providing instruction at an institution of higher learning should not require a degree from an institution of higher learning? That's deeply cynical.
How is it cynical? I don't believe "sports coach" is a job that requires a degree. If anything, it's pragmatic.
If we're going to maintain the gossamer thin connection with the actual academic function of a university, I think an undergraduate degree isn't too much to ask of a coach.
I don't think you necessarily need a degree to be a professor at a university, either, if your life experience trumps a diploma. Colleges and universities are not just about the degree. The degree isn't what everyone needs from these institutions and not everyone gets what they need from a degree. It's uncommon, sure, but we can point to an awful lot of people who were in college for a bit, got what they needed out of it, didn't finish, and were successful. Reggie Theus doesn't have a degree from what I can tell. That hasn't stopped him from success at NMSU and getting a job at CS-Fullerton.