I think they get a bad rap. Good scrum masters are worth their weight in gold at scale. The solve all inter-team comms, the bat away distractions, and they generally find the answers, or the people with the answers and get them solved and batted out.

Bad scrum masters take up space with reporting meetings that aren't reporting - but who are we kidding. I've been privileged to work with both.

For 19 years of career I've never met this unicorn scrum master you are describing.

Not a counter-argument, just sharing an anecdote.

Anecdote -- in the last 15 years I've had exactly one unicorn. They do exist, but they are very rare. And worth their weight in gold, I was really sad to lose ours in a layoff. Scrum masters, project managers, and marketing folks all seemed to be first out the door when money got tight

I thought the same of Project Managers, until I had the pleasure with work with the MissionCloud people in a project that included a Project Manager (in their side). I was amazed at her project management skills, and I really wished I could have her in my team.

That's the problem with anecdotes. Over my (longer, not that it matters) career I've had both. I've only had 2 of the unicorns however.

If the scrum master has enough rank or credibility + technical experience, they can get tickets routed and convince team leads that "yes this ticket is your problem until you prove otherwise".

This probably falls under your "solves all inter-team communication problems" catch-all.

They are project managers then, really.