Some questions.
Probably in all sports suffer to some degree from a rash of overuse injuries. But does any sport suffer more from it than baseball -- pitchers in particular? I'm guessing not. Maybe tennis? Swimmers?
Some sports you couldn't possibly play all year round -- you would be far too beat up at the end of the year. I'm thinking football, mainly. Or things like it -- rugby, possibly lacross. So presumably it's mostly non-contact sports that have morphed into being all year round sports.
Is the main reason to be a multisports athlete to prevent overuse and burnout? Or does playing multiple sports actually somehow help you play each one better? I'm not sure, but I suspect the former not the latter. It's not as though the skills you need to be an outstanding point guard have much to do with the skills you need to hit a 90+ mph curveball. (Correction -- that would be a 90+ mph FASTBALL -- not many guys throw their hook at 90. Actually does anybody? ) Ask Michael Jordon about that guards hitting baseballs.