Universities could pay for all of the research themselves theoretically considering they're the largest business in most states. Their portfolio income, the sports income, the donations, and the free real estate given to land grant universities that has been heavily monetized all add up. Of course I doubt they will allocate money to research, but they could if that was truely their purpose as an organization.
There’s could and then there’s should. Could they? I don’t know, I’d have to look at their finances individually, it’s not like all of them have Harvard level endowments or alabamas football income.
Should they? We literally built a juggernaut with our incumbent model that is the envy of the entire world and has produced untold innovation and wealth creation, for pennies of our tax dollars. The only reason I can see being advanced to undo that is pure dogma and blind faith in ideology.
I think a lot has changed in the last 20 years. It would be great if they could solve the problem internally, but it's already being run like a business. The innovation for pennies on the tax dollar is due to graduate student labor with pay in pennies on the hour to subsidize what is often commercial research that could be done by a company.