I did not take my gc out of my wallet except to show to INS, DHS, and after the post 9/11 security theater emerged, the DMV. Relatively rare compared to showing a DL or credit card.
Granted the DL is removed too many times from the wallet, such as for TSA theater, or showing at the exit of a rental
If you live south of I-10, or travel to any of the territories enough, eventually 100%.
I'd say at least once a week, I see post here or other places where an LPR forgot their gc before leaving the U.S. Seems more likely that will happen than getting mugged. Neither has ever happened to me.
I know someone who left his wallet with his gc, SS card (???), and DL locked in his car to go on a hike, and came back to find his car broken into to. That cannot happen to me, because I do not lock my wallet in my car.
These days my passport card has replaced my gc in my wallet.