The scarcity in Europe (at least the two countries I'm familiar with) comes from a standardized test. If you don't do well on the test, you don't go to college.

America used to do that, but Jewish students started taking (and doing well on) the test, and later Black and Asian students had the audacity to be brilliant too. This led to America's "holistic" college admissions process.

For what it's worth, the USA isn't unique in adapting admissions to reject an unwanted minority. The most interesting mechanism has to be Moscow State University's Jewish Problems: https://arxiv.org/abs/1110.1556