Rule 42: Supplemental discipline will be brought upon those who floss, brush and/or clean.
Made me think of how dreams of losing teeth, or your teeth falling out, are incredibly common, and related to feelings of powerlessness, loss of agency and control, depression, insecurity, and even recent grief.
Personally, I see this rule as the dictatorial regime and the MOAT wanting prisoners to put themselves in a vulnerable and meek state, where their teeth (literally the first weapon nature gives you, the first chance of autonomy that allows you to eat, one of the most basic functions of survival) are either ignored, dismissed, or made futile.
Which is doubly funny given that Draag's main industry is wheat, which requires strong teeth to properly chew and digest.