How would the German system work in the US case?
1. You'd go to the county seat/court house and register yourself. You'd fill out a sheet and they'd do a background check. If you've ever been arrested for threats or such (even with no conviction), that little threat will hinder your application. Threatened your ex-wife? You won't pass. Been convicted of some misdemeanor? No big deal. Convicted on some serious crime, especially with a weapon? Well, your application won't pass.
If you had 10,000 folks in one single country to push their application through....you can figure it'll take at least 12 months to get it validated. My best guess is that out of a hundred folks....maybe ten to fifteen will fail at this level.
2. Medical check. Your doctor will look over your records and determine if you have a mental disease or use serious drugs. Bi-polar? Schizophrenic? Cocaine-user? Opioid-user? You can figure your application will fail. I would suggest that 20-percent of Americans as a minimum.
3. You go and take a class on gun safety, and handling a weapon. Figure two Saturdays. The guys who accidentally fire their gun while in the class? You can figure they won't pass.
That would be it. My humble guess is that out of a hundred folks who currently have guns....thirty-percent would not get the license. Loss of the weapon? That would be the harsh reality, and I doubt that guys would be willing to accept this new reality.