This is something that the proponents of all electric-heating systems seem to ignore. Electricity is so much more expensive than any other method of heating, that it rarely makes financial sense. Heating electrically can only really be justified on environmental grounds, and that depends hugely on the mix of generation in the grid.
Historically, I believe the price per kWh of electricity has been around 4 times that of natural gas (in the UK) and around 3 times the price of kerosene. It varies quite a bit, but those seem to be good rules of thumb.
The table here is interesting reading. Ignore the actual prices as the data is from December 2021, but the general ratio between the sources seems to stay relatively steady over time. Anyway, according to that table, in December typical standard rate electricity was 23.65p/kWh, gas was 5.47p/kWh (delivered) (that's 4.3:1) and kerosene 6.69p/kWh (3.5:1).
Put it this way, in order for a heat pump to be cost effective against gas, it would need to be able to recover at least 4kWh of heat for every 1kWh of electricity used to run it.
Guess what? Despite what the brochure might say, it seems that air-source heat pumps struggle to be 4:1 efficient for more than a couple of months during the summer in the UK, and that over the year they could be as low as 2:1 (typically, I can't now find the report I read which put this into real numbers). I think we've had this argument previously. Space heating isn't usually the issue, it's getting your hot water to 55C or 60C that is the problem - heat pumps are less efficient the more they have to raise temperature and it's common in the winter for hot water to be provided by immersion heaters.
This means that (very roughly speaking and all other things being equal), swapping your heating from gas (or LPG) to heat-pump electricity will end up doubling your energy bills (four times the cost per kWh but 2:1 as efficient), and this is on top of the much higher installation costs. Oh, and now that the RHI scheme is finished, you don't get any government help either.
Regarding the original point (which may well have been tongue-in-cheek) while it wouldn't be worthwhile firing up F@H just to heat the house, if the computer is running anyway then there's no disadvantage. My NAS, printer, server Pis, modem and network switch are in a cupboard, and we have a central fan system which extracts warm, stale air from the kitchen, bathroom and this cupboard and uses a heat exchanger to warm fresh air coming into the building which is then piped to the lounge, bedrooms etc. For the few tens of Watts the fans take when running at "background" level, we recover most of the heat and distribute it around the house. Seems to work reasonably well :-)