In principal, you are correct, but you are neglecting one very important point: the government is not a nebulous entity with an endless supply of money. Therefore, the individuals that comprise the government must identify (either directly, or by selecting individuals who are most qualified in a given area of expertise to serve as proxies) the scientists whose ideas, proposals, past productivity, and requests for facilities most warrant funding.

Separating the wheat from the chaff is a non-trivial exercise. It may not be be direct innovation, but I would argue that it is every bit as challenging.