They should incentivize efficiency. In government, it would be citizen impact per employee. If you have more, you make more money, if you have less, you make less.
Do you think it would actually possible to quantify this in a way that:
1. Accurately represented "reality"?
2. Couldn't/wouldn't be gamed?
Seems challenging to me.
1) How many people are affected by the work of this agency
2) How quickly are peoples' needs handled on average
3) How pleased are people with the work of this agency
I think you could trivially measure each of those.
Choosing metrics to represent practical value, rather than let them be decided by profit-seekers, that's the real trick.
But if you make it annual standard operating procedure, then you are paying people to create spreadsheets and documents rather than, say, do something useful.
And the money will funnel to the people who are awesome at creating spreadsheets and documents rather than the people who are good at doing useful stuff.
Effective oversight requires understanding the domain and being motivated to continually improve things.