You guys are all correct.
Texas has mandatory yearly safety inspections, but you can still see cars that appear to be held together with rubber bands and spit.
I drove a '59 Edsel for years that had no seat belts and my excuse was that I was trying to keep it period correct, however I never really felt safe on busy streets or the highway.
Every other restoration or rod I have owned has had at least safety belts and the best brakes I could afford.