The US average residential electricity price is 18.07 c/kWh [0]. Natural gas is $15.39/thousand cubic ft [1]. 1k cubic feet of gas is about 300kWh (this varies because natural gas is not always the same and because the higher heating value and lower heating value are different. So the US average is about 5c/kWh of natural gas.
In decent weather, one should not use resistive electric heat — one should use a heat pump. In decent weather, a COP of 4 is about par for the course, making electric heat a bit cheaper. So I don’t believe your assertion that “gas is so much cheaper per joule”.
Obviously this varies by what you do with your heat and the conditions. Gas stoves are wildly inefficient, but induction can exceed a COP of 100%. In very very cold weather, heat pump COP drops, so gas will win. Gas tankless water heaters are reasonably priced and can reach well over 90% efficiency, whereas heat pump water heaters need a tank, which is somewhat lossy.
But gas has a major downside (aside from CO2 and other emissions): you need to pipe the stuff to the endpoint, and a lot of communities, especially new developments, have decided that this is not worth the expense or danger.
[0] September 2025: https://www.eia.gov/electricity/monthly/epm_table_grapher.ph...
I'm not sure what physics you're using to get a COP > 1 for an induction stove. I'm pretty sure you could put a Stirling engine on that stove and have a perpetual motion machine. Most of them run about 80-90% compared to 30-40% for gas equivalents, about 2-2.5x more efficient. And this is with expensive, high-end cooktops.
I think heat pumps make sense to use when available, but that's kind of separate from electric heat sources. If you actually have to source your heat from the power source itself, it's cheaper to get it cookies.
I have a heat pump on my house, but there's also a high-efficiency furnace and its COP is over 90% combusting gas.