Education has traditionally been a primary method for upward economic mobility. Once student loans became a thing, colleges jacked up tuition to put it out of reach of anyone but the super wealthy unless student loans were used.
People basically did remain in the economic class though. The school doesn't have much to do with it. Has class mobility significantly increased since the adoption of mass tertiary education?
And those who do not want to deal with the risk of going through school and not getting a better job to pay for the onerous loans can just remain in their economic class.