I mean to function without being babysat, not (only) from an economic perspective.
I'm not suggesting in any way a class-based education system, which are awful. I'm simply stating that if you are poor, your best bet is to pursue whatever education lands you the best possible job.
Why do you immediately separate eduction by wealth?
I suspect you mean that the purpose of eduction is to ensure that an individual can be gainfully employed and not be a burden on the state. One of your aims would be heading off any poor students pursuing a less lucrative degree (liberal arts).
This seems like a rather sad view of education.