If the entire team is discriminatory, then as the sibling comment said, metrics aren't really going to save you either, they will find a way to push their will through. And that is probably a horrible place to work that won't be made more palatable by being promoted.
Again, I'm not saying these aren't real issues, but relying solely on metrics is not the solution. You need both qualitative and quantitative data for a healthy environment and to make good decisions. Just because some humans are bad people doesn't mean the solution is to become inhuman altogether.
Again, we managed to do this for literal centuries without needing to turn workplaces into metrics-obsessed assembly lines. A manager should know what's going on in their team and should know who's doing well. It's kind of the whole point of being a manager.
But why on Earth is the total size of the organization relevant? That's the whole point of a hierarchical design, one manager just needs to know the people or abstracted teams that sit below them. Even in a "modern" org there's nobody sitting looking at a spreadsheet of 200k employees going "gee how will I figure out who to promote, better sort descending by lines of code written".
And yes, we've been talking in circles at this point. I agree a fully vibes based "promote who you feel like" approach has all those flaws, which is why I'm saying you need both quantitative and qualitative data. But in general qualitative should hold slightly more weight in complex, non-linear, interaction-heavy jobs like engineering, because it's hard if not impossible to find fair metrics for literally everything an employee possibly does.