Possibly. It's the only way it actually works though, because of the Peter Priciple.
Imagine the other way - you have peopel dong a role, and the people who do the best job at that role get promoted to the next one. Some of them will be good and the new role, some of them won't. The ones who are good will carry on getting promoted. The ones who aren't will get stuck in that role. The problem is that everyone rises to a point at which they can't do the job, and every role is filled by someone who has been promoted one step too far.
In a healthy structure, it should be a halfway house - you shouldn't have to be doing the whole job that you're trying to get promoted to, you should be doing enough bits and pieces of it that you demonstrate that you CAN do it. That way the company has information that they're not promoting you to a position of incompetence.
Imagine the other way - you have peopel dong a role, and the people who do the best job at that role get promoted to the next one. Some of them will be good and the new role, some of them won't. The ones who are good will carry on getting promoted. The ones who aren't will get stuck in that role. The problem is that everyone rises to a point at which they can't do the job, and every role is filled by someone who has been promoted one step too far.
In a healthy structure, it should be a halfway house - you shouldn't have to be doing the whole job that you're trying to get promoted to, you should be doing enough bits and pieces of it that you demonstrate that you CAN do it. That way the company has information that they're not promoting you to a position of incompetence.