If you have net metering, then buying a sizeable battery bank is in the same category as buying a generator - a depreciating asset mostly going unused.
If you don't have net metering, then you get bitten by needing to massively oversize your solar array to still fill the batteries on the worst case dim winter days, so that you can make it through the next night (likely powering necessary heating loads). That overproduction is then wasted on peak days unless you can find something clever to do with the excess electricity.
I'm sure there are other scenarios with time-varying electricity rates, but I'd think that calculation would be much closer to general time shifting with the backup power as an added benefit, rather than revolving around the backup power.
I think it would be interesting to consider partial or hybrid solutions, which may vary by climate zone. I.e. a solar battery setup that can cover typical day/night cycles with a tuned amount of excess, with some "survival" mode where you conserve battery charge for longer outages.
You'd need some pre-planning to segregate different circuits to do partial transfers and/or some smart appliances which can operate in reduced power modes. In the survival mode, maintain a critical baseload of lighting and food storage, perhaps even with some freeze-proofing heating mode that does not hit regular comfort targets. Use high-load equipment only when there is excess solar input beyond what is needed for battery maintenance etc.
You could also provide the right kind of exterior input to allow a portable generator to be added to the system in an emergency situation. This could support higher peak loads or recharge batteries when solar input is insufficient.
No heating loads, it's a natural gas furnace. Loads are just lights, furnace blower, and other ancillary loads.
It's not exactly the same as just adding battery backup, because the marginal cost of adding battery backup to a solar inverter is far lower than getting an inverter for just backup purposes, and solar allows a smaller battery.
If you don't have net metering, then you get bitten by needing to massively oversize your solar array to still fill the batteries on the worst case dim winter days, so that you can make it through the next night (likely powering necessary heating loads). That overproduction is then wasted on peak days unless you can find something clever to do with the excess electricity.
I'm sure there are other scenarios with time-varying electricity rates, but I'd think that calculation would be much closer to general time shifting with the backup power as an added benefit, rather than revolving around the backup power.