First off getting shit on your hands should be way more rare than that. Second off, if you don't wash your hands after using the restroom then when do you wash them? The point of hand washing in the bathroom isn't to clean shit off your hands (usually), it's to clean all the other dust and gunk and germs from the past 8 hours of opening doors and shaking hands and such. Your hands are disgusting even if they don't have brown goop on them.