Sounds like you work at a pretty toxic org if this is the case. Even at Amazon a big component of management promotions is how many people did you get promoted this year and what are the highest levels of people reporting to you.
The fastest way to go from Senior Manager to Director is to get as many people as possible promoted to Principal Engineer, or hire more PEs. Or better yet get your Principal Engineer promoted so that they have to become your peer.
And you can guess what shenanigans result from such a strong incentive. People should be promoted when they are ready, not when their manager’s empire-building aspirations will benefit.
People were promoted after they were ready, because they had to convince a promo committee that they were ready. The manager was your advocate but did not have a say in if you were promoted beyond being your advocate.
So the incentives were aligned. The manager was incentivized to put you up for promotion as soon as they thought you might be ready, not the other way around. The toxic part was actually that your manager didn't have final say.
Even when they thought you were ready they had to convince others in an overburdensome process.
I don't think what you wrote and I wrote are at all in conflict. I said managers are incentivized to promo people and that it's super hard for them to do so, which means people don't get their promos when they should. But it still contradicts what OP wrote about managers being incentivized to not promo.
The fastest way to go from Senior Manager to Director is to get as many people as possible promoted to Principal Engineer, or hire more PEs. Or better yet get your Principal Engineer promoted so that they have to become your peer.