Sorry, Fossil, Monique, et al., but I don't think it's paranoid to be reluctant to carry something as hard-to-replace and confidential as the IDs you describe "at all times."

My purse and/or wallet has been lost or stolen at least 6 or 8 times over the past few decades, and it was a hassle to deal with that, but nothing like it would have been had my passport, birth certificate, etc., been inside.    Those purses/wallets have been stolen from the trunk of my locked car, the filing cabinet in my university office, a shopping cart (which I never left unattended), the seat beside me in a dance club, etc. My cars have been broken into a number of times; my houses never have been.   I think it's a lot safer to keep valuables at home when not needed.

It is partly BECAUSE I need my driver license or similar ID to do things like travel by air, cash checks, drive a car, make many credit card purchases, etc., that I would probably NOT take that ID with me if, for instance, I went to the beach or swimming pool or hiking in the woods and was not going to be driving.   

I consider it very repressive for a government to require that everyone carry their papers on their person at all times. Might as well inject a microchip into everyone when it's considered a crime to have to tell an officer, "I left my ID at home," if you weren't driving.