> You can provide the piece of paper at a fraction of the cost

This isn’t socially useful.

Did Europe find a cheat code that gets free $$$ for education?

Nothing is free - once you graduate you are hit with 50% tax that gets back all you "free" tuition costs many, many times over.

Not saying education should not be subsidized via taxes (I think it's good overall), but it's not free at all - the price is just hidden and spread out over many years (similar to student loans but less visible).

That doesn't have prestige value. Prestige comes from scarcity and the ability to exclude the lower caste.

If people want to play those exclusivity games that's up to them. What's wrong is asking the taxpayer to fund it under the false mask that the entire product is education.