I would still have filed a report just to have more documentation for when they do catch the guy doing something else. If it was a parking garage in NYC, there are cameras. There may have been some identifying footage.
I carry 2 wallets. One that is larger and looks like a normal wallet that has no credit cards or IDs. It has photos, membership cards, discount cards. A small wallet carries my IDs and credit cards and is kept in another pocket. My cash is in a front pocket separate from both wallets.
I do like the way you document all of your cards and IDs. I will do that right now!