There are certain advantages that can only be won with the resources of nations. Even the most individualist nation has to act collectively in certain cases to achieve them, unless they are happy to see others take the lead. If we had not publicly funded the space race, for example, Russia would have won hands down.

When it comes to grand pure research projects, Quixote is right - there are considerable payoffs but not on a time scale that would attract enough private investment to get going.