The short answer
Because a degree is a fast, cheap way to shrink a pile of applicants when an employer can't see what any of them can do. It's a poor judge of skill, but it's quick, and nothing better has been on offer.
Economists call this the lemon problem. If a buyer can't tell a good used car from a lemon, they'll only pay an average price, and the sellers of good cars leave. George Akerlof described it in 1970.
Hiring works the same way. An employer reading resumes can't see what anyone can do. So they fall back on the signals they can see: the degree, the school, the years of experience. They treat everyone with the right paper as roughly average and everyone without it as a risk. Michael Spence described the other half in 1973, how candidates send signals to employers to show they're worth more.
The result is credential inflation. Joseph Fuller and Manjari Raman at Harvard Business School found that jobs done well for decades by people without degrees now list a degree as required. Entry-level shows it clearly. In an analysis of 95,363 postings, 61 percent of jobs advertised as entry-level asked for three or more years of experience.
Hiring software makes it worse. Employers told researchers their screening systems reject qualified people, and more than 27 million "hidden workers" in the United States are filtered out.
Notice who isn't the villain here. The manager with 300 applications and a day to cut the pile is doing what's sensible. The degree filter is cheap, so they use it. No one in the building has to want people without degrees to lose out.
The used-car market fixed its problem with history reports, inspections and warranties. Once buyers could see what they were getting, good cars could earn a fair price again. Hiring needs its own version: proof anyone can check.
If you hire for a role, write down what the degree is standing in for. Then find the cheapest way to see that directly, such as a short work sample, and put it where the degree line used to be.
This is an economic explanation. It doesn't prove what's in any one employer's mind, and some jobs really do need the degree: medicine, law, nursing. The 300 applicants is an illustration, not a statistic.
When employers can't see skill, they pay for paper, and capable people without the paper get passed over. The fix is proof anyone can check.
A good interview answers "which of these ten?" Something still has to answer "which ten?", and that is the job the degree has been doing.
A credential almost anyone can buy, and almost no one can fail, isn't proof of anything. It's a receipt.