Up until 1934, anyone could buy machine guns through the mail. Up until 1968, you could buy cannons and anti-tank weapons through the mail. Grenades were not illegal. Until very recently, you could walk into a store any buy explosives in several states. There did not exist any significant illegal activity with these items before they were banned to the common folk.
From the above, it seems clear that "the line" can safely be drawn somewhere above machine guns, cannons, and grenades. We are nowhere near a "reasonable" line.
The Bill of Rights guarantees the right to keep and bear arms. "Arms" are rifles. Cannons, grenades, and nuclear weapons are "ordinance".
The Bill of Rights works quite well.