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 provides all the energy anyone needs for everything with no limits. It’s one component with several good use cases.
So unless you have enough generation to completely decouple from the net you are not really independent or it will cost you.
So without additional Equipment just having solar and a power wall wouldn’t help during outages.
Yes you need cords, appliances, and other equipment, including extra equipment if you are not connected to the grid, that is a given.
[1] https://www.eia.gov/energyexplained/use-of-energy/electricit...