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.
In real world examples (places that get hurricanes, for example), the charging stations generally come back online before the gas stations. And an EV is way better in stop-and-go evacuation traffic, too.
> need a super long heavy duty extension cord to power my fridge
Why on earth would you need a heavy duty extension cord for something which pulls so little power?
I otherwise agree with the sentiment, however, it is way more convenient to set up your panel so you can backfeed it to power the whole house (or a nice chunk of it, at least). My Lightning will power all the important bits of my house for the better part of a week, all from the plug in the bed of the truck.
I would need a heavy-duty extension cord because I would have to run it 60 feet from my garage all the way into my kitchen. I also have no idea how I would actually plug the fridge in because the power cord is hidden way in the back.
That it would be more convenient in the long run if I could backfeed to my panel, but almost no EVs in the U.S. are actually capable of this. The F-150 Lightning that you have is quite unique in this regard.
I have absolutely experienced the “run on the bank” effect on gas in areas under hurricane warning, as well as weeks afterwards.