You should have that right. Though how would you feel if in order to practice with such weapons you *had* to go to a range to retrieve your weapons that were held in a locked safe at said range? Or you could hold such weapons yourself, being trained in their use via the military, but had to transport them to the range in a locked safe.
You'd still have the right to own and shoot such weapons, just not quite as freely as you have today.
What if gun ownership laws were tied to national service. Say for example joe public was permitted to own at most a small calibre, manual (i.e. not auto/semi) handgun for "self defence" or was permitted a low calibre rifle/shotgun if they were registed members of a shooting club, or needed the weapons for their work, say hunting.
If you wanted access to bigger and better weaponry an individual would have to serve in the military for a minimum of 2 years.
There are a plethora of options on gun laws available.
As gumboot has said more eloquently than I can. The ability to hold guns for self defence and the perceived need of the majority of the people in the US to have a gun for self defence is the fundamental difference between the gun control laws as they exist in the US and other countries.
The US has a unique gun culture, it also has some of the highest rates of violent crime, and gun death in the western world.