Harvard could easily build that out of their own $40,000,000,000 endowment, if their first priority was actually education, rather than protecting their own prestige and the value of their credentials to the elites they mostly serve.
This is another impediment he didn't mention: a sort of regulatory capture working on the social level. Harvard's prestige begs the question of why people want to go there. None of the interested parties want to change that, because it's to their advantage. To provide a Harvard-level education to millions (not simply academically, but to open the lanes of opportunity in all ways Harvard provides) is to destroy Harvard. But then, one wonders what the utility of Harvard is to the average American.
I don't know if it would "destroy" Harvard, but it would definitely make prestige more "merit" based (merit being in quotes because its definition is highly contentious). If Harvard were catered to all students with capable ability and/or drive then we'd have a new class of highly paid professionals. The problem as I see it is with funding. Will the state by itself be able to uphold the funding that supports the infrastructure and academic resources researchers and students need to succeed? Those who were admitted to this merit-based system may contribute, but that leaves room for the incentive-based system that we have today
Trends that hit the black community tend to follow in the working class and, later, middle class and wealthy white communities, perhaps under different circumstances but ultimately similar in nature. Compare the crack/cocaine epidemic with the opioid epidemic, for example. While I support the expansion of elite education, I think it's naive to expect it to be a panacea. Someone still has to see enough value in these grads to hire an order to two magnitude mire highly-paid professionals than there were before. Save some other concurrent intervention, what's more likely is that you'll have more highly-educated underemployed workers than ever.