What do you think many of homeless carry around with them ? Their driver's license ? Their CC permit ?
If I'm not driving, I'm not carrying concealed, there is no need for me to be carrying an ID. Often when I walk my dogs.... I don't have one on me. There is no requirement for me to carry "my papers" .... to prove I'm a citizen either..... so ..... why would more be required of me than an illegal alien in our country ?
That would be a rather fun legal argument..... which I'm betting they would lose. I can think of a lot of attorneys I know that would love to take that one on.