If you want people to push to a test branch before master, just set your CI/CD up in a way that enforces this? Build proper infrastructure instead of reinventing the Stasi with more Black Mirror.
This is like counting LOC all over again, but worse. As soon as you introduce a metric, (some) people will do anything to win. Make a clique, cheer each other on an hourly base. Introduce a bunch of typos on the about page, tank the penality, fix each one as a separate bug. My points triple whenever I hit 10 green commits? Brb, setting up a background task that checks whether my commit was green and if so deploys it 9 more times. Good use of dev time and resources!
Who looses? Your silent wizard dev who could not care less about social gratification and (used to) work on the big picture instead of fixing an endless stream of trivial bugs.
I also disagree with the notion that you can/should outsource manager-dev interaction to such a program. If an engine can trivially measure a dev faux pas, it can also just prevent it in the first place. If something unforeseeable goes wrong, you need the "human friction" as you call it. Why? Because you want to actually unroot the root cause (call it 5 Why's or whatever) and not just finger-point someone, and you certainly don't want to tank someone's social score for it.
Please look at a database of engineering/software disasters. People die because engineers are dis-incentivised to speak up, challenge security assumptions or break things. Sometimes that includes testing stuff a whole week w/o pushing anything (which you punish) or breaking something (which you punish).
Sorry - the idea is well presented and your landing page is nice - but IMO this software somewhere between useless and harmful...