We should absolutely ensure that people get a quality education and that the rigor of the programs are aligned with the difficulty of the field of study. There's nothing wrong with having 'weeder' courses early on to ensure that people are capable of completing the program they are in.
That is different from "competitive" admissions. Which, in my interpretation, is artificially limiting the number of admissions such that perfectly qualified (or overqualified) people are rejected for nebulous reasons (i.e., not a "good fit") in an effort to maintain prestige.
> It's worth noting that many colleges have even more remedial mathematics courses, which (no joke) cover elementary school stuff. E.g. the standard algorithm for division...
Mathematics education sucks in most of the US. In large parts of the country, how far you're able to go is determined by how well you do in your math classes at like 10 years old. If you do poorly, then it's very likely you'll be stuck on a tract that will never teach you to solve linear equations. Those that do well end up learning integral calculus before college.
Additionally, you have to consider that returning students may have not had a math class in a decade+ and it's hard to know where to start everyone. So it makes sense to start people from arithmetic. My mother went for her degree in her 50s and literally started at Kindergarten math and worked her way up from there.