Private capital is good at funding research that is likely to provide a short-term return on investment. It's not so good at funding basic research, where most of the paradigm-shifting breakthroughs come from. These provide a huge return on investment, but it nets out to society at large on time scales of decades or centuries.

Contrary to what you said, there is actually quite a bit of private philanthropic funding for research, it's just that it's not evenly distributed. The vast majority of it seems to go to medical research, in particular cancer and Alzheimer's. That's obviously a good thing, but my point here is that we can't necessarily depend on private philanthropy to distribute funds optimally.

https://www.cato.org/blog/governments-should-not-fund-resear...

I'm generally a fan of Cato and a libertarian approach to economics, but I'm still not convinced that we should be spending zero public money on basic research. I would like to see a decent amount going into mathematics and theoretical physics for example, and I doubt those fields would stay afloat on donations.