I'm pretty convinced that there's no set of metrics that can effectively capture productivity and business goals without being gamed. It seems to me that the only effective management system is a "web of trust" style system where middle managers have a lot more autonomy to make decisions based on their own judgement. Unfortunately it's hard to legally CYA if something goes wrong with that kind of setup and it has other vulnerabilities like being manipulated by sociopaths.
Overall, managing people at scale is always going to be a hard problem and it seems unlikely that technology will ever offer a satisfactory solution.