Maybe cost would be at some point but its not right now.
Plus I suspect your taking some extreme case here, heating a house requires a lot of energy. I'm using 50 or so KWH of gas right now and even taking efficiency into account thats probably putting 40+ into my house.
Adding that via electric would likely be more efficient but its already seen a load of the efficiency impact taken elsewhere hence the higher price.
It was even on the news today, despite GFCH being cheaper if you need to heat up a local space its often cheaper to boost it with electric fan heater or similar as whilst they are considerably more expensive for larger volumes of heating they can be effectively efficient in some smaller cases.
Part of the issue with GFCH is its be design designed to take a lot of energy and release a lot of energy, so you need to use a decent amount just to get the system up and having an effect.
I tested it.
I put on the CH for 2 hours, it hit a peak room temp of 16.4C towards the end but most of the period was lower than 15C (ambient temp of 12C), really struggled to get the temp up, in those 2 hours it consumed an extra 31.2KwH according to smart meter.
So a cost of around £3.10 rounded down a bit. (10.24p KwH)
I then put portable heater on and adjusted it to hit 16C, not only did it get it there very quickly, it was also blowing the heat at me so I felt it much more, it used up around 1.4 KwH extra for those 2 hours.
At a estimated cost of 46 pence. (33p KwH)
You seem to have put more effort in to understanding this than others, so I hope you can understand the rationale here.
I am not wanting to use the heating for long periods of time (as you said GCH has a cost associated with starting up/warming up), and I dont care about heating areas where I am not there as I consider it a waste of money. On top of this my property has really bad heat retention so it needs something capable of blasting out heat in a targeted area to overcome it. The rest of the room away from the blast of the heat may not feel as warm, but it doesnt matter as I am not in those other areas.
Every single thing I have watched or read about GCH been cheap seems to be based on a ton of assumptions.
Typically the following.
Property has good heat retention (double glazed, insulation etc)
Modern boiler
Room thermostats
Good piping and radiators
Exposed radiators
Requirement to heat the whole house
Wanting to use it for long periods typically at least 6-8 hours. (cost per hour goes down the longer its used)
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I am going to test cost of electric blanket wrapped around body. Probably will work out the cheapest of the three providing it can get warm enough.
There also seems to be no scientific measurement of the amount of KwH needed for gas to heat vs Electric, essentially they are assumed to be the same efficiency and they quote lower gas unit prices as meaning its cheaper.