

Adding batteries to a device has one advantage: portability. It also has mutiple disadvantages: batteries add weight, add design complexity, and make it more difficult to fully shut off power in an emergency.
Major household appliances aren’t portable, and are subject to failure modes where you really do want to cut all the power right now and make sure it stays that way. Thus, the disadvantages of adding batteries directly to an appliance outweigh the advantages.
A power wall using this new battery tech would be great, though.
Appliances have potentially serious failure modes that don’t involve battery fires. (We had one here a couple of weeks ago, which would have flooded out our basement if I hadn’t been able to cut power to the pump involved.) Being able to cut the power completely and instantly is not negotiable for a lot of appliances. I wasn’t even taking battery fires into consideration when I wrote about failure modes—I was talking about things that already happen to plug-in appliances right now.
Yes, the added weight and complexity are likely not all that significant here, but they’re sufficient that, even without the power-cutting issues, they outweigh any benefit of attaching a battery to the appliance directly. It’s just not a particularly useful idea when you get pretty much the same benefits with none of the downsides by incorporating the batteries into the building’s power system separately.