If every gun and every bullet were marked, all sales (or losses e.g. to theft) required registration with a central registry with the new owner requiring a proper license (including criminal background check, etc.), and distributors/manufacturers/registered owners were held liable for damages in the case of improper use, and with potential for their ownership/distribution license to be revoked, guns would become a lot safer. (Exactly what breakdown of liability is up for debate, but currently there is none whatsoever.)

Almost nobody has a problem with “gun ownership” in the abstract, and some type of gun ownership is legal in most parts of the world. The problems are with e.g. semiautomatic rifles being purchased on the black market and then used to shoot up schools, criminals trivially and untraceably getting their hands on as many guns as they want, people leaving guns lying around in places where children can play with them, or huge numbers of untraceable guns getting smuggled across the border into the hands of Mexican drug cartels.