Even if an antigunner accepts some highly regulated gun ownership, it is only for self-defense and then they see no "need" for more than one gun. They accept and see guns only as weapons. So a "sporting purpose only" gun buff or gun collector with more than one "instrument of death" scares the bejeebers out of them.
I have shot guns since I was six, owned guns since I was fifteen, and bought guns when I was sixteen. I started with plinking with .22, then hunting, then civilian marksmanship, military history, muzzleloaders, back to hunting, and finally convinced by two detectives and a corrections officer that self defense was a legitimate reason for owning a gun.
So I own more than ten guns, and have seen national gun control groups raise this "arsenal license" idea before, and I would hate to see it revived again.