They keep their rifles at home UNLOADED, the ammunition is kept at the local army camp. They can retain the weapon when they finish their reserve service and only after stringent checks and licensing something that seems to be sadly lacking in the US
A rifle without ammo is an expensive club.
Licensing is the first step to confiscation. You should know that from your own country and others.
Our press likes to tell people that there are no background checks for weapons purchase, but they lie. The gun show loophole is a lie. Gun shows follow the laws of the state in which they are held. It is true that some states do not require background checks for private sales. That is the choice of the state. Any licensed gun dealer does checks. They are done through the FBI.
There are some issues that should be addressed. For instance, the kid who shot up the school in FL would have been denied a purchase if law enforcement in FL had done their job and arrested him for his numerous prior law-breaking incidents. Why didn't they? Because that county is run by leftists and they were trying the kinder, gentler, type of law enforcement. The kid had no record even though he had menaced with a firearm before, so there was nothing to show up on the background check.
So yes, if you want to tighten things up, starting with enforcing current laws would be a good idea.
None of the crap being proposed would have stopped any of these shooters. Most gun crimes are done by people who don't follow the law in the first place, so they are not going to go through a background check to get a gun. They'll just buy one off the street that has been stolen and it will be a handgun, not a rifle.
It's going to get worse, not better. They are letting people out of jail at a rapid rate. Not prosecuting violent crimes. Not keeping those who need to be kept for mental health reasons. That's why gun sales are up so much. We are on our own until it gets as bad as it was in the 70s and the leftist elites start feeling the impact.
You saw how quick they were to protect themselves in DC. Let a few of them face muggings and break-ins and they'll start to get the picture...unless their armed guards protect them!