There's something wrong with being a gym teacher? A lot of young people who realize they are good enough to play college ball, but not good enough to play pro, choose to coach and teach at the high school level.
I think there might have been, but completely different majors. Sports management is more admin, where as phys ed major (going into teaching) would require a lot courses on learning, development, classroom management, assessment, etc. You couldn't get teacher certificaiton from sports management.
And btw, I'm not necessarily arguing for a PE major, just saying it could be done.
Some of the best mentors I had in high school were my gym teachers and coaches (often they were both). Some great lessons learned from my track coach after practice while bsing in the locker room. They were often the ones who had the flexibility to treat you like men.