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.
Any good university will have a limit to how many students it can absorb. A professor can't teach 1000 students in a class, not well. So you either have a university that can accept ~any number of students and function as mostly a diploma mill; or a university that actually cares about teaching students and thus must have a selection process.
Of course, there is some room between these extremes, especially for unpopular subjects where you hardly even get enough students to fill up a professor's time. And in those cases, you'll also see that EU systems will essentially accept anyone. Typically, for uncompetitive universities and subjects (majors), the only condition is to have passed (gotten at least 50%) for the local equivalent of the SATs - a very low bar.
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.