The FAA (and, prior, the Civil Aviation Authority [CAA]) has regulated aircraft manufacturing for more than 50 years, working hard toward making all aircraft as safe as they can be. In addition, the FAA requires periodic inspections, certified mechanics, and other rules that ensure public safety. To their credit, aircraft that are properly maintained and repaired last a very long time. Many pilots fly small aircraft that are older than they are.
The flip side is that if cars were required to follow the same rules, new vehicles would cost $100,000 or more and engine overhauls would be required, by law, at, say, every 100,000 miles. Driving would be much more expensive, and not necessarily that much safer.
All civil (nonmilitary) aircraft require a current airworthiness certificate stored in a visible location somewhere in the plane. It includes information about the manufacture and certification of the craft. To get an airworthiness certificate the plane must be built in an FAA-certified factory to approved plan standards or, if homebuilt, inspected and tested by an FAA official. Certifying a new aircraft design and the factory in which it is built can be very expensive (read: many millions of dollars). That’s why few really new designs are coming out of aircraft plants today. Most are simply upgrades and enhancements to designs that have been certified for years.
So how did light-sport aircraft get around the need for certification?
"Man cannot discover new oceans unless he has the courage to lose sight of the shore."
-- Andre Gide