That's not true. In organizations that have these kinds of parallel tracks, advancement for managers is DIRECTLY tied to their ability to promote engineers on their team.
It's an aggregate effort. If you can't promote engineers that report to you either have * Limited soft skills * Inability to attract quality engineers * Inability to take ownership of projects of significant complexity
In any of those cases, how can you promote a manager like this?
Managers are ABSOLUTELY incentivized to advance the careers of their reports (the good ones at least, but should this not be merit-based?)