There are aptitude tests of some kind and quotas for all good universities everywhere in the world. Harvard won't admit 100k students in a year if they randomly decide to join, nor will they accept a student without a stellar record (apart from legacy admissions, of course). And I would bet you whatever you want that you'll get a much better salary fresh out of college in Europe with a bachelor's from the Technical University of Munich (total cost: around $2000 if you're a citizen of an EU country), or TU Delft in the Netherlands (total cost: around $9000) than you will in the states with a degree from a random college that doesn't even have to bother with admissions tests.
Sure, if you're a brilliant young mind and can get into Harvard and qualify for assistance with your tuition, you're set for life, basically, in a way no EU university can match. But for the vast majority of the population, the outcomes are significantly better with the EU system.
Also note that the gigantic tuitions at US universities are actually a relatively recent phenomenon (and a similar thing happened in the UK). Even in the 50s and 60s, tuitions were much closer to the current EU norm.
