It has two or three roots.
Various court rulings have made it illegal to use IQ tests and the like as a criterion for hiring, which is what some companies used to do, if the tests produce racially disparate results. The problem is that nobody has been able to come up with a workable IQ test that doesn't produce such results. So a lot of companies started using bachelor's degrees to take the place of the tests, letting college act as a sorting screen.
Another reason is that the elite classes in the modern West are very comfortable with academic thinking and academic testing and such, and so tend to favor that route to join their ranks, or screen out others. It's become a subset of the whole credentialism process that guards access to the high levels. This is also reflected in the stigmatization of 'the trades'. One of the ironies of our current elite class is that many of them hold mechanics and carpenters and plumbers in contempt as intellectual inferiors, but some of those same people couldn't replace a car battery if their life depended on it.
Add in the fears of parents who don't see any other route to success for their kids, given the high immigration rates and technological changes of the last 30-40 years, and you've got the system we've got.