But there is always some metric to be gamed. There is always some causality chain which results in a specific distribution of money to organizations. Just because we close our eyes, it does not make the causality go away.

This doesn't necessarily mean that the system is gameable. If we suppose that what we're measuring is actually exactly what we want to get out of the program, then the only way the program can get ahead is by providing more of what we want. The system can only be "gamed" to the extent that there's a divorce between what we want from it, and what sort of output we measure.