I wouldn't carry a passport unless out of the country.

A lot of travellers carry a colour photocopy of their passport (stored separately of course), and have another one accessible to a family member or trusted friend. This helps your country's embassy or consulate issue an emergency passport quickly.

I suspect that in a genuine disaster, a passport photocopy in combination with other genuine ID would be worth having. It might help grease the bureaucratic wheels that grind so slow.