The answer isn't to be more fair about how you select people for your exclusive school. The answer is to make the school and its resources not scarce and exclusive.
Most people aren't really there for a liberal arts education; they're there to try and secure future employment.
Support apprenticeships and on the job training alongside online courses and universally accessible community college.
It won’t happen without a significant cultural shift either. There seem to have been a number of institutions that have attempted to make education affordable and they all fail for various reasons. One being that at the end of the day a college degree is the only sort of credential considered respectable and even those can be worthless depending on a number of factors.
Also, the number's probably more like hundreds of thousands or perhaps millions when you look internationally.
Another issue is that the degree is valuable because it is selective and admits high quality students who will be high quality professionals as well. If a larger population is admitted because they can do the coursework but they are not quite at the same tier of capability, the value of that diploma will reduce.
On your second point: a Berkeley diploma signals that a graduate (1) is above some minimum (but still very high) threshold of competence, and (2) has a level of competence governed by some probability distribution that's above that minimum threshold. I assume that as Berkeley admitted more students, the minimum standard would stay the same but the average of that competence distribution would decrease toward that minimum.
This is subjective and I'd understand if you disagree but that seems like a worthwhile tradeoff to me. I think there are pretty few jobs for which a bottom-of-their-class Berkeley CS grad is underqualified, and obviously those jobs have their own evaluation/screening processes on top of looking at the Berkeley diploma anyway. I suppose an employer looking for the "superstars" in the top 1% (by some immeasurable criteria) of their class at Berkeley would have to identify the top 0.1% instead (if we generously assume that Berkeley's current admissions process never turns down those students), but I'm less concerned about those dozens of students than about the tens of thousands more who could benefit from both a more rigorous curriculum and the ability to demonstrate to employers that they're above that minimum threshold.
that won’t change.