There are many industries which have found value in specific people to do the paperwork and deal with process. I don't think it's needed under 10 or so people if you have a good team, but once you're we'll into the 20+ range, I don't understand why so many devs are so set against giving this type of work to someone else.

It's certainly not what I want to to be doing day-to-day, yet our tools aren't smart enough today for me to do well in a larger org without it.

Funny you say that while every other "expert" says it's pointless to do scrum above around 10 members.

Not that I believe any of that eh, scrum usually devolves to ritualistic, empty blabbering in around six months anyway.

Yes and no. On the useful side, they own some of the process inherent in large organizations. But they also act as a conduit to push that process to team members.

In practice, our scrum masters have been a place for the PMs, Analysts, and QA leads to go as their positions have been displaced. I would like to see more technical scrum masters that can own technical impediments, but that doesn't seem to be happening yet.

I also think that spreading scrum masters across teams will disconnect them from the specifics of the work and allow them to act more as coaches than non-technical team members.

Yes absolutely, a good one is invaluable at helping the rest of the team be more productive.