The important thing is that these things get funded. It doesn't matter what institute funds them. If an institute becomes stultified and corrupt, there's no reason to champion it over creating another.
Are you implying the NIH is "stultified and corrupt"?
If so, care to back that claim up?
So no, not all things government does can be replaced by the private sector, for reasons of game theory.
Trying to fix the world with a sledgehammer.