I live in a place with sensible firearms laws, so this is totally a thing. Gun owners are licensed, and part of that license is a "good character" and "legitimate purpose" check. Self defence isn't a legitimate purpose, so if you start running your mouth on Facebook about shooting people on your property there is a tip line people can send reports to, and you can expect a visit from the local police. Similarly, getting caught DUI will violate the good character requirement and you'll need to surrender your guns - you'd better be able to account for all of the guns registered in your name or you'll end up with a much more serious conviction
Most of the world doesn't even have guns for their citizens. But I have switched my opinion a little bit on this topic. I used to think nobody should be allowed to have a weapon at home. But after seeing the constant failure of police departments to protect people, and the increased crime levels, I now think it's actually not a bad idea to own a gun. Nobody else is going to protect your family.