The school I attend is 60% foreign students. It's a larger percentage at the graduate level. As such, I don't particularly feel like I'm taking advantage of the system. Rather, it feels like the system is actively trying to encourage people to study there.
First, most countries in Europe do not have free/ cheap tuition for non-EU students. I think it's mainly Switzerland, Germany and a few others. Out of all the Americans I've ever met, I've only known of three others who've done a graduate program in Europe. Two studied in the UK and Ireland, so cheap tuition was not a thing for them. The third was an American whose lived in Switzerland for a long time. Her family does pay taxes.
Graduate degrees in the US are often paid for by the university as well. A very large proportion of our graduate students are international students. Those that study my field, statistics, would generally be paid by their university. For this reason, studying in Switzerland is actually more expensive for me, as I have to live off my savings.
It's not easy to study in Europe. I had to live at home and work to save up money. Most of the graduate programs are not in English, which provides a natural barrier for most Americans, and graduate programs have stricter requirements here. For my fellow Americans, they require that you have taken exact classes and have a bachelors in a specific field. There's not much flexibility. Also, the bureaucracy is insane. I also study an "in demand" field in any country. Because of linguistic restraints, most Americans who study in Europe study "in demand" fields, as they are the only ones in English. And they're in English in order to attract international students. Also, Swiss schools fail students at a much higher rate, so it's a risk to come here. It doesn't seem beneficial to me that the government funds so many students to start degrees they never finish, yet they do.
Finally, I study statistics. Literally all the data we use in class is gathered from US sources. Usually, this data collection is funded by the US government. My classes are also often taught by representatives from companies who receive tax breaks from the US government. In addition, the US provides a lot of funding for the creation of STEM resources that are used internationally.
TLDR: It's hard and expensive to study in Europe. American tax payers pay for international students to study in the US too. Many of the resources my university uses were funded by US tax payers too.