The problem isn't measurement, it is tying rewards to achieving certain measurements. People will do what you reward them for doing, even if that isn't what you actually wanted them to do.
The real issue is that identifying the correct things to measure and reward is really, really hard.
I read once about a factory that was trying to improve output so they started rewarding shifts of workers for reaching production goals. But to achieve those goals workers started cutting corners and quality went down. So the company installed a device to measure the quality of the widgets, which worked for a while but then quality went down again. The workers had figured out they could just keep measuring the same in-spec widget over and over again to make the machine happy. Next the company altered the quality measurement machine so that it would issue an error if it did two identical measurements in a row. Again quality went up for a while until the workers figured out they could just rotate a couple of good parts through the machine to fool it.