I thought about this a lot while working at a high-growth company recently.
Decided that regular (quarterly) manager rankings (HR-supported, anonymous) by 2-3 levels of subordinates is the only way to solve this at scale.
The central problem is: assuming a CEO accidentally promoted a bad middle manager, then how do they ever find out?
Most companies (top-down rankings-only) use project success as their primary manager performance signal.
Unfortunately, this has 3 problems: (1) project success doesn't prove a manager isn't bad, (2) above-managers only hear from managers, and (3) it incentivizes managers to hack project success metrics / definitions.
Adding a servant/leader skip-level metric is a critical piece of information on "On, this person is toxic and everyone thinks poorly of them, despite the fact that they say everyone loves them."