Degrees are a big part of the whole class/job circus
In the US, student loans are a huge drag on the average workers income. Yoshomon, in personal conversation, mentioned that in Kentucky, the average person with a university education now was projected to have less take-home pay (pay minus loans) than a person who'd never gone. It seems like a logical possibility. A bank has loaned you money to turn into "human capital" and so you only own the bare labor you would otherwise be able to contribute. With an exact enough calculation, capital could get every level of professional making only slightly above minimum wage.
I remember also a news item that claimed a lot of college fees paid for things like research and administrative apparatus. It certainly doesn't seem like it would be hard to main professors and classrooms for a lot less than American university costs ($30K+/year).
Also, I'm not sure I would want to classify education as simply a necessity or a luxury. Certainly, those are the categories generated by capitalist relations but the world is more complicated than this.
DW