I like your football game metaphor!
The gun registry did not work in Canada. Your idea seems to have some component of a regsitry. There will be less compliance in the USA than there was in Canada.
Tying a firearm to its owner will have more bureaucracy that Dave Tomlinson's idea. I prefer to keep things simple when we can. Citizen has a firearm in a clear possecion + citizen has no license = firearm is confiscated. It won't matter if the firearm is owned, borrowed, or stolen.
Even Dave Tomlinson's system is not perfect. Some bad guys and mentally ill people will find a way to get a firearm. We are only reducing, but significantly reducing.