Chicago has electricity prices 25% lower than the national average. If you want to see an example in your area, watch Technology Connections heat pump videos on YouTube.
Alex is a smart guy, and he makes a lot of convincing agruments in favor of heat pumps, but the thing he consistently sweeps under the rug is that for about half the US (and all of Canada), the annual cost to run a heat pump sits well between a natural gas furnace and resistive heating. And the further north you go, the more it shifts to the right. I run the numbers every few years and for my specific house, I'd pay 30% more to run a heat pump instead of a furnace. (Before factoring in the cost of the unit itself and installation labor.)
Where I live, the only way heat pumps make economical sense is if natural gas gets dramatically more expensive, or if solar gets cheap enough that every household can afford a roof full of solar panels and a basement full of batteries. (Which to be honest is kinda my dream situation anyway.)
The house (built just a decade ago) feels much better insulated now.
If you do the exterior walls yes, but most heat loss is through the attic and roof. Air sealing and super- insulating the attic floor is pretty cost effective. Likewise sealing cracks around windows and doors.
Why is that? Maybe I'm missing something fundamentally, but this should be a strict function of COP, $/kWh (elect.) and $/kWh (gas) right? The insolation thing is kind of red herring, because that saves kWh-needed and that goes into both, right?
And yes COP will probably be bad/worst on some days of the year. But on most days even Chicago should get a pretty decent COP from a low-temperature heat pump. Is natural gas just so cheap in Chicago?
heatpumps are not expensive but they are not cheap COMPARED to other alternative. cop is not constant, it changes. closer the outside temperature and indoor temperate is, less work is needed / higher COP heat pump provides.
buying 4 times more panels gives you always 4 times more energy. in -40F you get 4 times more energy from 4 times bigger pv array. heat pump will probably just start running integrated resistive heater IN THESE temperatures.
heat pump can be configured in a way that it not only heats but also cools, so yes in that situation heat pump can be cheaper. then not having one and be less comfortable / productive because of it.
you can buy PV system and after it paid itself, it still works, still generates electricity. gas can not be 0 $. so depends what / how you calculate things.