Hold on, what incentive does the EU have to allow US citizens to just go to the EU, get a 4-year education, with full room & board, and then possibly head back to the US? Color me skeptical.
My university (in Denmark) had a large number of eastern European students it created a very different environment, a better one in my opinion. Students are exposed to different ideas, different approaches to solving programs and learn to work together with people with a different background and culture. Of cause my university focused heavily on group assignment and working in groups in general.
I honestly don't mind that my tax money is spend on education people from around the world, although I think it's currently only free for EU citizens. And perhaps there's the added bonus of a few opting to stay and work in the country.
I am also in Denmark, and my university has a number of students from eastern Europe, Russia, South America, Iran, China, as well as those on scholarships from developing nations, and exchange students from the US and Canada.
(I suspect we may have attended the same university, as mine also focused heavily on semester projects (50% of the ECTS) and group work)
It's not a bad investment at all. But ultimately, it's about making sure the next generation has access to good education, and how can you really put a price on that?