Our best universities involve a symbiosis between the bright and the rich. They're famous for the talents of the brightest, which achieve their full extent because the rich paid... to be around this fame. This has, for a few centuries, been quite a productive system.

Other systems are possible, but they have other tradeoffs. You can for instance pay for everything out of taxes, but this means putting those in control of the tax system in charge, and they have their own interests. The extreme of this was the USSR, and it did great science in some areas. But was far from paradise.