The key with a generic degree is that it admits you to specialized training afterwards, or careers with on-the-job training like civil servants. In the US there are this many people in these jobs that have any 4-year-degree as their entrance qualification to vocational training:
3.2 million teachers.
2.8 million civil servants
1.35 million lawyers.
0.25 million military officers.
Those four alone are around 5% of all the jobs in the US (7.6/155 million).
I think there's quite a lot, when you count the jobs where there's no specific degree requirement but HR/recruiting/middle managers will express a strong preference for candidates with degrees. Maybe not explicitly but their choices aren't usually rigorous to begin with, so such biases can easily creep in.
