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.