When we understand a role to be "someone who manages the events" - it's inevitable that people will pass that role around in a team. What's the big deal? You can hold the Daily Scrum today, just make sure we keep it to 15 minutes & everyone tells us what they're up to.
Right?
The short response to understanding is, no that is not the ScrumMaster role.
I mean facilitating events & keeping to a time-box is certainly important in serving a development team. Just that you're only scratching the surface of what the role actually is.
Some hints for you would be to think about the 3 services a ScrumMaster provides. If you're throwing the role around like a badly wrapped present at a pass the parcel birthday party - you're just about touching the 1st service, which is service to the team.
There's quite a few examples to unpack on what happens when we rotate the SM role & I add a little more colour with examples on the clip below:
Thanks,
Jem :)