Everyone understands that public services are free to use because they are funded by taxes. It's not the gotcha you think it is. People say that roads, K-12 education, etc are "free" when they mean there is not a direct fee to use them because they are paid for by the government using tax dollars. You don't have to pretend to not understand this
Elsewhere, you worried that getting millions of people put of crippling debt due to a broken education finance system might tick up inflation.
Here, you worry that making society more educated via university training might decrease the economic value of a degree.
Where is the humanity? Of course some extreme of inflation is bad, and of course we want people to be employable. But artificial scarcity seems like a bad way to go about it.
(And I don't think we have a surplus of engineers in the country, judging by what I perceive to be the gap in talent between china and US, and the moaning by tech about the need for H1B).
Also if you are being $ focused then offer it where there is ROI: STEM, medicine (allow more doctors too).
Education doesn't lose its value if it is free. Does food and water? Shelter?
Unless people are just tuning out of their degree and it is just a social thing. In which deal with that specific problem.
It sounds counter intuitive, but more taxes is more fair and better as a whole. To prove, it takes no more than to look up correlation of amounts of taxes with percentages of homelessness (and other such indicators) between western countries.
Does health insurance also lose its value when anyone can get it for free?