Worth considering: if you own a truck you have to register it and get insurance in case you cause any damage. Even ignoring the effect on killings, it doesn't seem unreasonable to ask the same of gun owners.
No, you don't, at least in many ag-based US states. You can own and operate a truck without a license or insurance on private property. Which means nothing would stop someone doing that, and then driving it on the roads and running people over other than a cop being lucky enough to pull them over first.