You joke, but it’s reasonable to not brush. Sugar causes cavities, not lack of fluoride. Try a year without brushing; see for yourself.
DONT DO THAT. If you do decide to follow this crazy advice, please keep flossing. And keep going to the dentist every 6 months. I wouldn't want to get a freaking root canal (or lose teeth) from a misguided experiment like this.
Fluoride is just to help strengthen the enamel. You can brush your teeth without it. In fact, there were some amazon tribes that used a kind of tree bark. Works fine, I tried it.