There are a few explanations here. The first thing to note is there is not much of an addressable market of people who would go to the EU for education. Low income students (<100k income) would not have to pay much in the form of tuition, and high income students (>300k income) likely have enough saved in education plans to afford the education. That would leave only middle income students who might consider going to the EU, but these students would likely favor state flagship schools or schools with scholarships considering career outcomes in the US.
The second point is that most private universities are charging what people are willing to pay. For "admission" into high finance, academia, or medicine where people can garner very high salaries, going to a "prestigious" college is a huge advantage. People are therefore willing to take out a loan with the chance to make it back many times over in their mid to late career.
And finally, the reputation of academia is mostly defined by outlier research academics, not undergrads or tuition pricing. As long as these universities produce outlier intellectuals and intellectual capital stemming from these universities, they will be able to charge much higher rates without losing anything.