Primarily, unlike the US we just lack the void space. Even if you're in a "rural" area you'll still annoy dozens of people firing a spud gun with compressed air, and one fired with explosives will be thought of as someone firing guns - which is damn rare to hear, only during hunting season in the forests. The same argument also holds valid for a number of other things common in the US but not in Germany like keeping entire residential properties filled with cars in various states of (dis)repair, firing guns in general, producing nuclear waste, flying experimental planes, starting planes and choppers from anywhere else than a licensed airstrip, ...
The reason why it's never gets fixed for the US must be that the US also has total global socioeconomic dominance and none of you guys want to rock the boat and accidentally fix that too in the process.
The Nordic countries are not far behind on gun ownership, and I recently learned (I have my gun background from mandatory military training + farming/hunting, so mostly bolt action except in military) that even semi automatic are still very accessible than I assumed, you just need to know how.
The Czech Republic is even more liberal than that.
Several European countries also practice the storage of military weapons at home, actual full auto assault rifles meant to defend against an invader.
So again: the difference I think is more in culture than in the amount of weapons. Obviously control makes a difference as to who gets hold of the weapons, but again, the rules are pretty lax: a good reason (hunting and/or sports shooting), and, in the case of sports shooting (at least for single hand guns) a recommendation from a local club.
The American culture were guns are stored loaded around the house however and the glorification of gun violence, that however scares me.