Haven't seen the show, but it sounds like you have a good point.
On the other hand, I think a lot of these post-apocalyptic stories are not really meant to be realistic. They are meant to deal with our primal fears. We have this great civilization that keeps us safe from the elements, but now and then we can see the cracks in the facade, like after Hurricane Katrina. So it's fun to ask, what if the whole house of cards came tumbling down, never mind the details?
For instance, just working in the library, it was only twenty years ago that we were finding all our references on paper card files. Nowadays we have access to a lot more, and more quickly, but when network outages happen, as they do several times a year, we are basically helpless, other than going out to the bookshelves and browsing. And when we have actual electrical blackouts, we can't even wash our hands or flush the toilets in our building. That's how dependent we have made ourselves on electricity. That kind of insecurity is what shows like Revolution play on.
So yeah, if we really did lose all electricity, we would probably find a way to muddle through. But who wants to watch a show about muddling through? We want grand drama and adventure!