During the end of a dry summer, large swathes of California have the power intentionally shut off for days at a time if moderate to high winds are expected. In those cases there is no emergency at all, so using a car battery works great.

As to your concern about the house losing power when you go on an errand, that is pretty much a non-issue because losing power for an hour or two will not cause food spoilage, unacceptable HVAC conditions, not depleted batteries in flashlights or electronics.

As far as range anxiety, I think it really depends on the location and types of expected disasters. For example where I live the top concern is earthquakes where you may need to flee a fire. In that case even just 10% battery will get you well away from the impacted disaster area to somewhere you could charge back up. In a place with hurricanes that calculus will be very different and this solution may not be a good idea.

As to your concerns about battery wear and replacement costs, I’ve been hearing that line since I got a Prius in 2003. The problem was way overstated then, and is even less of a concern now. With the exception of truly terrible design (Nissan Leaf) battery packs are very well managed now and will last quite long for the average user. In addition, almost no pack actually needs total replacement, there is now a robust and mature industry around refurbishing packs and replacing only the cells that have actually gone bad in a pack for significantly lower cost than total replacement. That industry will only grow and improve as the EV market expands.