From your description and context, it sounds like you're describing elementary algebra and not abstract algebra.
Honest question that sounds mean: isn't elementary algebra required for graduation from high school and admission to university? My university didn't offer elementary algebra, and I thought students without elementary algebra skills needed to at least start out in the community college system. In my public school system, the advanced math kids took elementary algebra in 8th grade, and the less mathematically inclined took it in 9th grade.
Where I taught, they gave the incoming freshmen a math test, and the kids were put into Calculus, Algebra, or a "remedial" math course. Algebra was the lowest level course that could be offered by an accredited college, and the "remedial" kids eventually had to pass Algebra.
This was a large state university, so the kids came in with a wide range of skills, from a state where there is a lot of variation in how math is taught in high school. They were bright, affluent kids. Many of them had taken algebra and even calculus, had gotten good grades, but had not really learned those subjects well enough to skip them in college.
I had pretty much the same thoughts as you express, but as the semester progressed, I developed the opinion that these kids had been screwed by the system and still deserved a chance. They were not going to be engineers. Most of my students were planning to major in psychology or business.
Honest question that sounds mean: isn't elementary algebra required for graduation from high school and admission to university? My university didn't offer elementary algebra, and I thought students without elementary algebra skills needed to at least start out in the community college system. In my public school system, the advanced math kids took elementary algebra in 8th grade, and the less mathematically inclined took it in 9th grade.