That was my concern, too, albeit not the biggest (which was range anxiety)....until the day 2 years ago when a windstorm took out the local Grid for 3 days. Not an extensive amount of time, but it was the first time I had really worried how to recharge my car. After a certain amount of panic (but of course) I decided to see how widespread the outages were in my neck of the woods. Turns out it was pretty extensive with about a quarter of the Commonwealth of Virginia in the dark, but not everywhere. And those "not everywhere" places weren't that far from me AND had charging stations. A great sense of relief, to be sure, although I was miffed to not being able to charge at home. The closest "lights still on" was my favorite grocery store in a town 12 miles up the road. The closest "Level 3 fast charging" was 24 miles away, a pay to charge EVgo, as was my Nissan dealership 32 miles away with the free fast Level 3 charge.
So I went about life as usual. The gas stations in the blackout areas were closed with signs up. No electricity meant they couldn't pump gas. It would appear none had pre-thought about emergencies with a backup generator. They didn't appear bothered by hanging "closed " signs on the pumps, and going home. Fortunately the fire company and EMTs were in the "lights still on" zone, so no worries by them.
I decided I would do a late night shopping trip and plug in my car at the free Level 2 in the grocery store parking lot. I took a good book with me and relaxed for the 2 hours (Level 2 is a mere 7kWh) it took to recharge back to 100%.
I haven't been bothered since.
Now, a hurricane would wreak havoc on more widespread areas, but honestly if the Grid is down, that affects gas stations as well as residences. We have a number of neighbors around us that have the whole house generators that can easily recharge an EV while still running all the electric for the houses. It is easier to truck in a large generator for an emergency station that to try and deliver fuel with all the attending risks. And when fossil fuels are a thing of the past, solar panels will have already long been crowned king for our source of electric power
I agree that it is going to take time for all the nuances involved in the infrastructure to be sorted out and dealt with the most efficient way possible.
"The world ..it is...a-changing.