I don't believe that Hinckley deserves to be described with as friendly and positive a term as "gun nut".
A lot of people are nuts over classic cars , guns , objects of art, antiques , et cetra, this is usually positive and constructive, at worst is possibly wasteful.
Hinckley was empowered by a rather non-interesting gun, his choice of ammunition was a mistake for his purposes. Thank God for a bit of well placed ignorance.
Background checks are generally regarded as reasonable , even the NRA supports them, but who is responsible for putting people on the blacklist?
Any measure can be carried past reasonable limits, there are anti-gun nuts in existence who would put practically everyone on the blacklist.