I noticed a huge problem at a FAANG in a 40 person team and proposed the design of a single metric that incorporated all costs including countervailing metrics.
There were no takers for the project. The senior manager leading 4 teams of 40 engineers told me privately.
Your proposal is relatively cheap to implement and I can't ask for more HC for this and doesn't help me with empire building.
Your metrics will make the team achievements look smaller and weaker.
Your metrics will anger many of the teams, because the team switches the metric to target each half. In your example, targeting customer throughput one half and customer satisfaction the next half thus running a merry go round. The team has become comfortable switching metrics each half and it is simple work.
If your metric is set as a target, the engineering problem becomes a lot harder and ICs will be upset.
So, my proposal was canned.