I think a sensible option, if you live in a place where electrical grids goes out for a couple of days fairly routinely, would be a transfer switch and a generator. If sized well enough you could use it to run a resistance heater (the cheap portable type) to keep one or two rooms warm in an extreme scenario.

Pipes freeze and burst, whole house has to stay warm. It’s not just about comfort or safety.

If you warm up a few rooms to comfortable then it's hard to imagine the rest of the house being at freezing temperature. It's going to be some sort of gradient. But sure, this is a concern/consideration.