That's exactly what they did at my college (non-California state school) 20 years ago. Special program for students from poor high schools who otherwise wouldn't be admitted, where they came in the summer before freshman year and had to pass some prep classes first. IDK what the actual long term results were, but seems like a better idea than nothing.
Under the circumstance that the primary and secondary education levels have failed to adequately prepare a student for tertiary level, I think your idea would be unfair.
The university teaches what it teaches; it exists as a place of higher learning. If the student is unprepared for that, they are unprepared to attend. It's not university's job to fix shitty high schools' teachings and redo lower learning. Go get a highschool tutor if you need that.
If you were never taught math, that sucks, but you shouldn't be admitted to a university. That's just not what needs to be happening. Go catch up on math at your own and reapply when ready.
It's difficult to assess which students have a chance of success without standardized testing.
"In 2024, over 25% of the students in Math 2 had a math grade average of 4.0".
Math 2 is the remedial elementary and middle school math course at UC SD. Lack of standardized testing plus grade inflation contributes to this outcome.
The latter may need an opportunity to succeed.