Earlier quoted context omitted.
Very much depends on the home. Tesla Powerwall 2 seems to be 13.5 kWh at 114 kg. Energy consumption can be anything from 30 to 40[1]. So one Powerwall 2 unit probably won't get you through the day if you use that much. [1] https://www.eia.gov/energyexplained/use-of-energy/electricit...
Getting you through the day is not really the point though. The point is 1) shifting some consumption during peak hours off of peak rates and 2) having backup to get you through a limited outage, not necessarily at your full normal consumption level but without having to be in the dark / without internet / without phone and possibly car charging. Nobody should evaluate this by whether one battery pack by itself provi…
So unless you have enough generation to completely decouple from the net you are not really independent or it will cost you.