In most places in the US, in normal working conditions, Heat Pumps are 30%+ cheaper than a gas furnace to run.

However, in some really cold places like Chicago, Minneapolis, etc - the days where current heat pumps are inefficient might be enough to make it cheaper to always run gas.

OP is proposing to have both systems and only run the gas furnace on extreme days - which would lead to a ~30% reduction in running costs.

I suspect the CapEx of having two heaters wouldn't make sense, though.

It'd be better to just have a hear pump that can run efficiently at colder temps.