There are a lot of “it depends” here. I’ve worked at orgs where best engineer gets promoted to manager because… best engineer! And the result can be a train wreck. I’ve seen the reverse where managers from a business background are managing engineers (also can be a train wreck). There are also plenty of great managers who don’t “lead”; they go about their work building a great working environment and helping others succeed (often a senior engineer will be providing the leadership portion).
A good organisation will be good at offering opportunity to the right people and giving them the tools they need. I agree that a good org is rarer than it should be, which is probably the source of much cynicism.