Public schools in the US vary from "absolutely atrocious" to "absolutely great" depending on where you live. The colleges that select students only from the latter do not waste time re-teaching high school material.

I think I did not express myself well. The problem I was referring to with the schools is not that some teachers are better and some are worse, class features, etc. This matters, but there are bigger problems as US lacks a uniform school program. The selection of materials is done more or less at the teacher's discretion.

This means that even in the same school the math teacher for kids entering grade 8 does not know what material was covered before. Some kids may have been exposed to a particular topic, some may have never seen it. So teachers have to go over the basic material again and again and again, which makes it very hard to give a solid course.

In Europe (at least in some countries), there is a standard program, so the teacher in grade 8 math knows that all prerequisites have been seen by every student. So they give a very brief refresher at the beginning of the year and can turn to the new material. Even better, when a topic is covered in a physics class, the physics teacher knows that the corresponding math tools have already been covered in the math classes.

Every state I've lived in has official curricula standards required by state governments, and the AP courses that are typically recommended to college-track students are standardized across the entire country.