Sure, as long as you size the system to expected loads.

An 8kW generator suitable for occasional use is only ~1,000$. A Powerwall 3 does 11kW continuous and peaks at 30kW for transitory loads like starting heavy equipment.

The most convenient solution where a generator automatically kicks in during a power outage requires an electrician and extra equipment, but there’s also real tradeoffs to having gas lines going to your home.

There are models that include a battery to reduce the input power requirement. That's not quite the same as the question, but it answers it, you just need a big enough battery and they are fine.

There is a good technology connections video about building backup batteries into the actual stove.

I think part of the problem with whole home backups is that they tend to be sized to a maximum load that is unusual or could be avoided with some effort. And that providing a backup for the essentials you actually need is relatively cheap and uncomplicated if you make some modest sacrifices.