Thanks for sharing your thoughts Matt.
In response, I'd say that for some students, your suggestion would be perfect.
However, studying, e.g., physics in a foreign language takes something difficult and makes it near-impossible. To avoid that, most American students would be limited to English-speaking countries or at least schools where English is the teaching language.
Next, you'd have to consider the extra costs of travel and possibly higher cost of living (depending on where you go to school).
Finally, you have to consider that most 18-year-olds aren't really mature and self-reliant enough to safely live overseas and away from their family support system.
Also, there are relatively inexpensive options in the US. For example, in-state tuition for public universities may be around $20k a year.
Even better, you can attend a community college for less than half that for two years, and then transfer to your state's public university until you graduate. Your degree will still be from the state school, but your 4-year cost might less than $60k.
I'm not sure how many decent European universities would offer an American student a less expensive degree.