I can mainly speak for Sweden, but basically the answer there actually is ”everybody who wants to and meets the minimum requirements (essentially having graduated high school)”

Sweden has higher gross enrolment in tertiary education than the US, and a larger proportion of older students (people who go back later in life to progress their education or change paths)

I’ve heard that in countries like Germany people are often ”locked in” by choices they’ve made at an early age. There’s an element of that in Sweden too (more vocationally-focused high school programs may not give you all the courses that you need to enter all university programs), but that is not too onerous to overcome if you change your mind later (you can do ”foundational studies” to bridge the gap, or just sit exams to prove that you’re qualified)

Edit: but it’s maybe also to your point that universities have limited seats, just like everywhere. Maybe your high school grades or score at the equivalent of the SAT aren’t high enough to study mathematics at the top-rated institution even if you’re qualified, because there are too many people ahead of you. But you will be able to go to uni somewhere to study something