In the US, there's already this.. https://seedfund.nsf.gov/

Not the easiest thing to get into though, and still capitalist-minded. And actually it's easier to start and maintain a for-profit company for research than it is a non-profit organization, so if you're going to have a for-profit company anyway then you might as well seek a variety of funding sources, which do include strings attached leading to monetization. It's just how the system is unfortunately...