

There are countries that do, but you’ll still need to demonstrate that you have the financial means to support yourself without working or needing recourse to public services for the duration of your study, so there’s still a fairly significant financial barrier to entry for most individuals. If you have the money to put down for 3 years of rent, food, utilities, etc, while you complete a degree in Europe, I imagine you’re generally doing pretty okay for yourself in the US.
While Catholics do have a lot of wacky beliefs, papal infallibility is somewhat more limited than this. It only applies when the pope makes an ex cathedra statement, so he would have to state this in a much more specific and formal manner to be considered undisputable doctrine.