The issue there is the plug would be on the battery which you're unlikely to have mounted in a convenient location for things like your main fridge, router, and computer. For me all 3 of those are pretty far away from the most likely places I'd put a battery bank. I have a mobile one I keep charged up for emergencies and long power outages and have a small portable solar panel for it for multiday outages.
Ah, right I was picturing an oversized car battery that you can lug around. Extension cord then? Not sure but this seems surmountable without having to rewire the house and get a permit or licensed unit for feeding the grid