There is recovery service to help out in emergency situations with cars, black outs don't last long and buying some food because you are hungry is just a convenience as long as you last meal was recently. However, if you raise $100 in a fire to lure a fireman to get you out first or place well known banknote with a message for help, I think this is when cash is used for survival.
Having said that, I usually carry something like £20 for mini-emergencies/inconveniences, but it changes once I travel abroad because £ usually goes further than local currency. Nowadays you can get cash and card payment almost in any popular place. And if they don't have electricity, it is still not a problem - they somehow get a copy from your card and cash later. Card fraud protection makes sure only legit transactions get through.