Should asking job applicants about college degrees earned be illegal?

Scott Alexander has a rather interesting alternative to plans for free college:

“presidential candidate Bernie Sanders has proposed universal free college tuition

I’m afraid that Sanders’ plan… would subsidize the continuation of a useless tradition that has turned into a speculation bubble, prevent the bubble from ever popping, and disincentivize people from figuring out a way to route around the problem…

If I were Sanders, I’d propose a different strategy. Make “college degree” a protected characteristic, like race and religion and sexuality. If you’re not allowed to ask a job candidate whether they’re gay, you’re not allowed to ask them whether they’re a college graduate or not. You can give them all sorts of examinations, you can ask them their high school grades and SAT scores, you can ask their work history, but if you ask them if they have a degree then that’s illegal class-based discrimination and you’re going to jail. I realize this is a blatant violation of my usual semi-libertarian principles, but at this point I don’t care.”

Credential inflation is a real issue, and it is good to see it getting more attention. I don’t know as though I’d go as far as to criminalize asking job applicants about their education, but there is a very good case to be made for legislation to overturn Griggs v. Duke Power (this Supreme Court decision largely outlawed skills/knowledge tests administered to job applicants, likely leading to greater reliance on education credentials and hence fueling credential inflation).