> In America you can get into university (even a prestigious one) and start off at "College Algebra."
It may be possible to get into any given University and start off with college algebra, although I'm not entirely sure about that. However is certainly not the case that you can get into any program at any University and start off at college algebra.
Admission requirements for majors are determined by departments responsible for those majors, and they can and do set their own standards for what is acceptable when declaring that major.
For example anything remotely related to Stem at any of the UC schools is going to expect that you have, prior to entering the program, already completed at least the equivalent of Calculus BC, and usually linear algebra as well, in order to be accepted into the program. If you're starting off at college algebra in one of those schools you will never complete the math sequence necessary to start one of these programs and still graduate within 4 years.
True for some universities. My university (Top 30 overall, public) does not consider intended majors as part of undergrad admissions, supposedly. Now, it would be practically challenging for a physics major to start at algebra and get up to calculus soon enough to start the physics classes, but no one would stop you. A few majors require an application in the second year, but those are specialities like journalism, business, library science, not regular STEM majors (except CS as of recently).
It may be possible to get into any given University and start off with college algebra, although I'm not entirely sure about that. However is certainly not the case that you can get into any program at any University and start off at college algebra.
Admission requirements for majors are determined by departments responsible for those majors, and they can and do set their own standards for what is acceptable when declaring that major.
For example anything remotely related to Stem at any of the UC schools is going to expect that you have, prior to entering the program, already completed at least the equivalent of Calculus BC, and usually linear algebra as well, in order to be accepted into the program. If you're starting off at college algebra in one of those schools you will never complete the math sequence necessary to start one of these programs and still graduate within 4 years.