My take is the SSN isn't needed. There is only one of me at me address, so unless there is another Alan G. with fake ID to support that he lives at my address it should all be good
They've got your full name, place of birth, date of birth, gender, race, and state of residence.... Don't think they don't know exactly who you are before the page gets flipped to "what is the type of firearm?"...SSN or not.
I am with the OP on this. I work in a Trauma Center and we are drilled on privacy or better yet HIPPA as its known...Sometimes cannot be helped but all reasonable attempts should be taken to protect all info as much as possible. I know of several shops that use an alternate area to call the checks from and even if a customer has to wait most would understand. Personal preference but if you have ever had your identity stolen it is a pain in the butt...This comes from having it done to my wife. Some call me paranoid I just call it heightened awareness. If in the future any concern about the customers privacy should be expressed before filling out 4473 and usually seller will attempt to accommodate I would hope. Just my thought.