If there's a charging station with power within 200 miles then you're fine. That's a pretty big radius.
If power is out in that large of a radius you would also likely have trouble getting gas.
And you don't need the expensive equipment to just run an extension cord from the EV to power critical appliances.
If there's a charging station with power within 200 miles it will be overloaded by everyone freeing. There are way more gas stations than charging stations, and they only take a few mins per person, so they would not be nearly as overloaded. Also, there would not be a "run on the bank" mentality since everyone knows gas is pretty available, even in emergencies.
As for powering critical appliances, I'd need a super long heavy duty extension cord to power my fridge, and I don't even know if my vehicle is capable. I'd also have to have my garage door open while it's plugged in, which is not ideal to say the least.