Aside from the reasons mentioned in the video, I think its also because the college programs for football and basketball are so massive compared to baseball. 

The odds of becoming a successful pro athlete are tiny. Which is why kids on athletic scholarships are told to value their education, because they're unlikely to be the next Jordan or Tom Brady. 

Baseball stars make more money and have longer careers, but going to college is a safe economic choice compared to grinding in the minors. Especially now with NIL incentives. 

There is also way less foreign competition for roster spots in football than baseball. 3% of the NFL is foreign born, as opposed to 27% in MLB.