A generator that can run heaters, even a heat pump, for more than 10 minutes, needs to burn natural gas or propane or gasoline or deisel. You can't store enough in batteteries.
Electricity serves as a backup for gas because it's the grid, or a generator, not a battery. A big generator works for efficient heat pumps, but in the all-electric future (if it comes too fast like now, before we actually have enough grid and better storage), there will be no generators or gas to fuel them. There will be batteties and solar that can do everything light and nothing heavy. Even with a generator, it needs to be a pretty big generator that most people don't have, and if you tried to use space heaters you could only use a couple small ones and you've maxxed out the generator. A big but not crazy generator can run a whole house heat pump, and that almost uses up the entire generator.
Whole house non portable generators can run on piped natural gas, which gives you not only heat but electricity while the power is out.
If you only have power, there is no effective backup for it, unless as I said you actually have an entire 2nd grid that duplicates the efgective entire 2nd grid that is the gas pipes. Different physical distribution infrastructure (so 2 sets of independant cables) operated by 2 different organizations, in 2 different physical locations (one buried, one not, whena truck takes out a pole, it doesn't affect the buried, when a backhoe or ice heaving takes out a buried, it doesn't affect the poles, etc)
That level of redundancy sounds outlandish but we actually have that right now, and will be losing it.
Maybe it's not valuable enough to maintain, but there is no way around the fact that it is something that will be lost.