The question is whether that means they are denied a good education, or just denied an education at their preferred school. Nobody is guaranteed an education at their preferred school, and it isn't reasonable to expect that everyone who applies and is above a certain threshold will get in, because there are limits in terms of housing, numbers of professors, etc.
In a zero sum scenario, where pretty much all schools have that policy, those students definitely do not receive as “good” an education because the schools with better funding and reputation become full. The system is no longer a merit based system, though with the nepotism and generational wealth dependence perhaps they never were, but it’s been sold as true.
Then magically make a bunch of housing appear in or around universities, because until you do that, there's gonna be scarcity. That's just reality. Scaling up staffing is doable up to the limits of the classrooms, but once you hit that limit, building more classrooms takes time and money, too. What you want just isn't realistic.
Perhaps not in a pure capitalistic sense, but many countries not only have free student housing, but free college as well. Further, college costs tend to be higher and there isn’t the same incentive to keep costs down with unforgivable student loans so colleges can just build and build unnecessary things and keep getting students to pay. You do realize how limiting education with artificial scarcity or scarcity through incompetence is bad for everyone, right?
It probably does reduce it, but doesn't permanently mangle it. See my comment above about how kids brought in by affirmative action do considerably better than predicted by their high school grades.
Yes because they quite literally are held down by their situation, instead of those who had every resource available and simply aren’t skilled and thus don’t deserve in a merit based system. But it’s also obvious they don’t perform as well as if they had resources from birth. LeBron would be amazing at basketball even if he was forced to not play or train till 18, I’m sure far outperforming the average person with that same history, but it’s obvious he wouldn’t be at the top of his game just as someone who was never properly educated because they didn’t have somewhere to sleep, or food to eat, or proper school supplies until college.