For a relatively small battery like that, it's not going to last for days. In the typical outage where that battery would carry you, you can typically just leave the fridge closed and it will stay cold enough to prevent 99% of your stuff from spoiling. For most people (at least the US), it's not super easy to get at the plug in the back of the fridge anyway.
Running HVAC is usually more of a concern, especially in winter or peak of summer, and those aren't device that you can hot-plug, and a small battery wouldn't help there anyway.
I like the idea of whole-house batteries, but to really make it practical you're talking about thousands of dollars to the battery, install, etc. And you still don't have extensive run time, which is why I think you see most people still leaning towards permanent or portable generators way more than batteries.
Running HVAC is usually more of a concern, especially in winter or peak of summer, and those aren't device that you can hot-plug, and a small battery wouldn't help there anyway.
I like the idea of whole-house batteries, but to really make it practical you're talking about thousands of dollars to the battery, install, etc. And you still don't have extensive run time, which is why I think you see most people still leaning towards permanent or portable generators way more than batteries.