You're misunderstanding the problem. It's not that the UCs are admitting a bunch of special exceptions who failed out of high school math; these are people who got decent grades and are supposed to know the material.
Well, then. In that case, the simple solution is to admit more students in the first year, and aggressively flunk out the ones whose performance does not match their high school grades.
Why is that better than just requiring the SAT, which while imperfect does a great job at weeding out students who have A’s in math but can’t solve 8th grade algebra problems.