I admit I don't know much about project management. So it's quite possible you're right, and most of the project management work is put on the team (for better or worse, I think it's for the worse, anyway).

But, what I think is crucial, is (at least for someone) to know the history. So if the scrum master is to successfully improve the process, he should have a clue about project management and what was tried with what result. Otherwise he will just rediscover Brooks (Fred, although Mel is probably also a possibility). And that's why it's bad to say things like you are saying, that scrum master is not project manager, because then you will get people who really have no clue.

But a scrum master really isn't a project manager. That's like saying it's bad to say that a stakeholder isn't a project manager. It's a completely different project role.