This is because Europeans believe our agricultural peculiarities are worth protecting from the disruption of unbridled economic influences. Countries like France, Spain, or Italy, protect their milk so they can protect their cheese, so they can protect their recipes, so they can protect their food culture (and revenues) at large - a differentiator in the long term.
Some of the EU's subsidies go to "agricultural peculiarities" or small producers of niche traditional foods. That's fine, you're still propping up demand for the raw materials - that milk is just as good as any other if it comes to a crisis.
Im a New Zealander and it used to be a thing I’d read about and feel frustrated. However dairy farming trashes your land and waterways. Selling milk and milk powder is about the dumbest use of the land we could have come up with and it had caused massive harm.