I'll add on to your point: moving up the IC ladder is often slow because it takes more to both become an expert in a field and to prove it to your leadership. Each step up the IC ladder is harder to actually obtain those skills, and harder to prove that you have obtained those skills to management.
On the flip side, the management ladder is more delivery focused (though not exclusively): are you getting your team to get their work done? It's somewhat easier to demonstrate success on the management side, and because you're leading a team, it's possible (though not necessarily true in most cases) for a manager to get promoted on the strength of their team and not their ability as a manager.
This doesn't discredit what you say. It does, however, explain why it's much easier to move up on the management ladder vs the IC ladder.