People don't need to brush their teeth as much they need to "brush" (massage) their gums. A centuries old adage to "brush you teeth" should really be "brush your gums": massage your gums to flush out the gunk between tooth roots and the gum tissue lining them. Otherwise that sliver of space becomes a garbage dump where bacteria will thrive, multiply ... and deposit a foul smelling waste. I think that space is the primary source of halitosis, and more certainly the place where gum disease starts.
If it's true that Beethoven kept immaculate teeth using a napkin, I surmise that he was actually keeping his gums healthy by conscientiously massaging bacteria food out of his gum/tooth space.