NCAA covers a massive number of sports. The vast majority of those who go pro in any US sport, first go through an NCAA team.
Think about a scenario in the current world: You're a pretty good golf player in high school. You commit to Stanford for golf and a degree in some STEM field. The school already has a system in place to make sure both are possible. You give high level competitive college golf a shot and realize you can actually go pro. After college, you do. And even if it doesn't work out, you've got a degree from Stanford.
And then there's your world: You're a pretty good golf player in high school. You go to college instead of the separate LPGA feeder leagues because it's the safer bet and your school doesn't have a system in place to make sure you can compete in both. Why would they? You never get to experience and thrive in the high level competitions and end up not going pro.
So many professional sports would get maimed with your model. After a decade the US would heavily drop on the world stage when it comes to sports.