You touch on something — situation awareness — that's an important piece of your "survival toolkit." Since it depends on what you see and what you hear going on around you, wearing headphones would impair your effectiveness. Depending on nature and severity of disaster, time of day, and neighborhood/area you're traveling, could mean increased peril.
Granted, the radio would presumably provide information useful to broader SA, but perhaps best monitored selectively.
Here's brief write-up on situation awareness, some of which you might find applicable.