The problem is the blackouts can go for lengths of time that would require impractically large battery installs. You can powerwall your way around a grid that frequently goes down for a few hours to a day, but one that may go down for days to months you are practically forced into some form of generation (solar or otherwise).

Batteries keep getting cheaper but are unlikely to get to where it’s more affordable to store a month’s worth of electricity than just buying some generation.

> if you owned a battery that charged off the grid and discharged during blackout periods

This wouldn't work. The reason isolated units can inject electricity back into the grid without issue is that they can observe frequency. If a blackout occurs, this information is gone. You need to perform a black start, which can't be done by isolated, uncoordinated equipments.

Depends on the length of the blackouts, if it's more than a day then solar panels will allow you to lower the amount of batteries you get.