When I got my Green Card I was reminded in my "Welcome Packet" to carry my Green Card with me at all times.

This is also stipulated on the USCIS website and has been for as long as I remember.

"A green card is issued to all permanent residents as proof that they are authorized to live and work in the United States. If you are a permanent resident age 18 or older, you are required to have a valid green card in your possession at all times. "
Link here

So I don't see what the big deal is. It's a condition of my permanent resident status that I respect- and I don't even live in Arizona