The constitution says "shall not be infringed" period. Gun laws are not intended to help honest people buy guns, they are intended to make it more difficult for everyone to purchase firearms. If you don't include all the information they ask for, you reduce your chances of getting approved.
Arizona does not require a permit to carry a concealed weapon but has a provision to acquire a concealed weapons permit. With that permit, no background check is required. You just walk in, fill out the 4473, show the dealer your permit and walk out with the firearm. Avoids being subject to incompetent people who have the authority to spoil your day. Should you have to do this? NO Is it constitutional? NO Is it reality? YES How do we change it? DON'T KNOW
This is the way it used to be in Washington state. Then our lovely AG and the Seattlites that know so much about how to govern changed it with I1639. Now, everyone gets a check, delay, and maybe we will let you have a firearm. If it is for an assault weapon (any semiauto firearm) you have to allow your medical records to hang out in space for anyone to see.
