My standard reply to that is it would make the outlaws easy to spot.
The guy who shot up the church should have been denied guns already because of his mental condition. He was already easy enough to spot. I'm not sure about the Vegas shooter but i'd be all for any measures that would have identified his dangerous tendencies. What we don't want to do is restrict reasonable gun possession from responsible people, but be able to keep them out of the hands of the dangerous ones.