I think most people are aligned with your thinking and would like for their kids to play multiple sports. It seems most of the experts at the highest level of sports agree that it's best for kids to play multiple sports. Yet I kind of feel inclined to participate in the lunacy.
In my kid's case (he's only 11), he been excelling at baseball, but also enjoys basketball. Realistically speaking I didn't pass him enough genetic material to make the high school basketball team. To get there on effort, he'd have to somehow get hooked up with the AAU team that feeds into Corner Canyon HS and really pretty much put all other sports on hold. But then, we kind of contribute to the problem by having our kid play fall baseball once the spring season is done. I can't deny that he's making significant progress in baseball by focusing on it for another three months and he does enjoy it. But the most he'll ever be able to aspire to in basketball is rec league.