If a company is so broken that promotions are decided based on factually incorrect information, there's nothing to do other than escape to a different company.

I'm talking about companies that are functioning okay, but they let the PMs drive what the team works on. A bad PM will send the entire team in the wrong direction and waste your time.

In the most extreme example, our PM would get distracted from the goals set by management and want us to do side quests all the time, so the entire team was constantly producing things that management didn't want while missing all of the things they wanted us to do. If your PM is the link between management and the team's directions, a bad PM will sink the team.

To me, this means that every traditionally run company (top-down) must be broken by construction. And indeed, I have never seen or heard of truly fact-based management.

The entire challenge with multi-level management is that you always play a long game of telephone with increasingly less technical people, which are unable (due to lack of time and understanding) to grasp the ground-truth facts without simplification. Thus, management based on hard facts is impossible in this setting, though it is a great theoretical ideal many aspire to.

In practice, doing so is very hard and people are lazy, so the "facts" can become so twisted as to be entirely unrecognizable.

No company is perfect, no team is perfect, no person magically knows what's right to do and has a perfect vision. Even if you get somewhere with the right team, right vision and right priorities, and you stick with them, the world will change and one of those will end up incorrect.