It sounds like that would be a pretty principled CEO—a rarity in any day and age.
Realistically, while cleaning the bathroom occasionally is fine, the CEO can’t be a full-time or even part-time janitor and still have the time to do their CEO job. Although, now that I say it, most of a CEO’s work is based around talking and delegation, and doesn’t actually involve being busy with their hands, so maybe they could just go around with a headset and hold meetings as they mop the floors, or have meetings with people while they wash dishes inthe breakroom.