Their primary role is to remove blockers. Most scrum masters that I've worked with were previously full-time project managers.

As Scrum Masters, they tried to turn their role into a type of project manager role. Rather than contribute in any meaningful fashion they tried to add pomp and circumstance to a process that should be incredibly basic and should just serve to get everyone on the same page.

They are great at getting in the way rather than actually focus on clearing distractions and things that would prevent developers from getting their job done.

When Scrum Masters are in a role, and understand that they are responsible for a very limited set of responsibilities I find that they are more effective because they focus on those limited set of responsibilities.

I think it's best if the scrum master has other responsibilities and also serves as the scrum master:
- Perhaps as a type of analyst role
- Management role
- QA
- Etc

I think someone that really understood what they were supposed to do as a scrum master and wanted to primarily work as a scrum master could potentially work on multiple projects to work full-time...the issue with that is that the schedule would then rotate around the scrum master — when the scrum master is there to serve the team rather than the opposite.