Thermal energy and electrical energy really are the same thing, not two different quantities that happen to be measured in the same units, like grams of lead and grams of gold, or your example of US dollars and Jamaican dollars. When you convert less than half of the chemical energy in the gasoline into mechanical work to move the car, the other 50+% of the energy is converted into heat. Carnot gives us a reversible conversion factor between them, but it depends on the combustion temperature rather than being some kind of constant, as in your Jamaican-dollar example.

Technically you can interconvert grams of lead and grams of gold one to one, too, but interconverting electrical and thermal energy is so easy that it happens all the time unintentionally.

MacKay does in fact cover the Carnot factor you're talking about; his Chapter 21 http://www.withouthotair.com/c21/page_140.shtml begins:

> In the last chapter, we learned that electrification could shrink transport’s energy consumption to one fifth of its current levels; and that public trans- port and cycling can be about 40 times more energy-efficient than car- driving. How about heating? What sort of energy-savings can technology or lifestyle-change offer?

And then he goes into not just household heat pumps, and their achievable coefficients of performance, but also municipal combined heat and power, which take that ≈50% of the chemical energy "lost" from thermal power plants as waste heat and pumps it into your house.

So, far from being ignorant of the issue as you seem to be implying, he presents a more complete picture of the issues than you are presenting.

Specifically for household climate control, I suspect that both heat pumps and CHP are much less relevant now that we have cheap solar. You can think of a heat pump as a way to reduce the amount of solar-panel area that you need to heat your house. The trouble is that solar panels cost €0.13 per peak watt, while heat pumps cost closer to €1 per peak watt, so it may be cheaper to "waste" energy on heating your house resistively with a nichrome wire than to use a carefully engineered heat pump.

For the purposes of energy use, they are not. Heat is fundamentally worth less than the equivilent amount of electrical energy, due to these efficiency losses (which are not just a technology problem). It's misleading to compare them at any point in your analysis unless to highlight the problem with the comparison.