It's not. I know one Yokozuna back in the 1950s (Yokozuna Chiyonoyama) tried asking for a demotion back to Ozeki, but was denied. Much easier to ask them to retire than demote them.
Can't the Yokozuna technically call one? I remember hearing Hakuho did it once before when someone did a hair pull.
edit: It wasn't his own match that time.
I would hope they all wear mouth guards, since they're essentially headbutting each other every match. I know I've seen at least one other rikishi wearing one a few bashos ago.