Bacteria floating around in your mouth by and themselves are not strong enough to get through your enamel (hardest outer layer of the tooth), but when bacteria are left around long enough they begin to stick together to form a biofilm. This starts as a soft biofilm called plaque. Brushing your teeth or scraping it will remove this soft biofilm without much effort. In left untouched, this soft plaque begins to strengthen and hardens into tartar.
Tarter is solid and no matter how hard you brush, it will not come off. That’s why dentists scrape it off with special instruments. This is the reason why tooth decay can’t be prevented just chemically (mouthwash), it has to be addressed mechanically (brushing/flossing). Mouthwash is not a rip-off though, it’s just more supplemental. For an average person, fluoride mouthwash is best unless your dentist says otherwise.