They operate at up to 400% efficiency and represent serious low hanging fruit for household carbon footprint reduction and the main barrier is education, so no I don’t think they are overrepresented.
COP: Coefficient of Performance. This is a ratio of how much you can augment the temperature for every unit of energy you put in.
Your best, most efficient top of the line gas furnace has a COP of 0.98. This means that, for every 1 joule of energy, you're getting 0.98 joules of heat energy. Let's say that, for easy math's sake, you pay $1 per joule for natural gas, so your operational cost for the furnace is $1.02 per joule. Yes, numbers are crazy town, but simple math for simple explanation.
A modern bog-standard heat pump has a COP of 4. The operational COP of the heat pump varies depending on the difference in temperature from inside to outside, but the vast majority of the state of California is going to operate at temperatures that can support the COP. Per your statement, electricity is 6x the cost of gas, so we'll say that every joule of energy going into the heat pump costs $6. This puts your operational cost at $1.50 per joule.
It's certainly not a "better deal", but the cost delta can't simply be measured by the cost of the energy going into the heating system.
That's a steady-state, best-case figure that is almost never achieved in practice. Very long run times and very low temperature operation is required to achieve those figures, and most homes are not setup to create those conditions. I'd not be surprised to learn that most 95+% efficient furnaces run at 90% realized.
That might give some terms to Google and find additional data.
Peak COP’s equivalent is closest to SSE; SCOP is closest to AFUE.
FWIW: in Oregon, buying the "renewable" power from the utility: the heat pumps we installed 19 months ago for house and water heating are almost exactly even with the gas appliances they replaced. If we ignore the $8/mo fee we pay to keep the gas line attached (for a grill and two fireplaces), they win by a tiny bit.
California might well be more expensive. But a factor of six is silly, that's just not right.
Source: https://shrinkthatfootprint.com/natural-gas-heat-vs-electric...
It gets away with this by admitting the error in the text ("The only caveat is that we talk only about traditional electric heaters. Heat pumps are another story."), but the numbers remain a lie.
In fact if you look at it, that site seems to me to be a for-pay blog. Most of the articles are just product "reviews", with the remaining stuff a mix of bland overview stuff and articles like this that seem to push an agenda counter to the presented theme of the blog.
Be careful out there. The internet is a wild place.
That said, it’s arguably really tough to compare these two heating systems objectively and you can’t take the advertised rating at face value necessarily. It’s not apples to apples. Electricity billing is complex and includes many more variables and gas is billed completely differently which adds to the comparison problem. Any comparison online ends up making many assumptions so of course we need to take that with a grain of salt.