What you say is all well and good, but the reality is that most gas appliances do not work without electricity. Your stove is about the only thing that can work on gas alone. The furnace, the water heater, the dryer, they all need electricity.

So you need backup electricity either way. And in the case of a furnace it's still a significant draw due to fans and/or pumps so to get multi-day resilience you need a big battery. Less than if it was a heatpump, sure, but this battery and inverter system will use all the same amount of electronics either way.