Compare to a stovetop where there's a big heavy pot between the element and the water, and it's not in complete contact with it. Also often the heating element is underneath a piece of glass.
You’re describing resistive stovetops, not induction ones where the heating element is the bottom of the pot itself.
> Also often the heating element is underneath a piece of glass.
These things under the glass do not heat anything. They are there to induce some electric current in the bottom of the pan you put on top, which actually does the heating.
Glass infrared cookers also exist, my parents had one back in the 90's before induction was much of a thing. It was touted as easy to clean (and looks cool)
They are mostly historical curiosities now, right? Not as cheap as simple resistive cookers, and worse in about all respects than induction ones.
They're awful though, I've only got one because I'm renting. The old school exposed spiral element ones are the best non induction electric stoves imo.
The efficiency loss of the electric kettle also gets converted into heat that heats up your home, energy doesn't just disappear.
So it is "heat your house by X at price of the gas heating" vs "heat your house by X at price of electric heating". And the price of old school resistive heating, not the more efficient heat pump.
And gas stove kettle is ~40% efficient but you get the other 60% back as heat in the surroundings, so the entire process is ~100% efficient.
Assuming you need that waste heat of course. In the summer that 60% inefficiency really is an inefficiency.
My last energy bill (including taxes and fees) is showing $0.124 per kWh electricity, and $0.62 per cubic meter of gas.
And yes, electricity prices in Europe are crazy right now. You can see some graphs here that show how enormous the spikes are compared to years of relative stability (no need to read the text; the graphs speak for themselves, and the y-axis starts at 0!)
Electricity: https://www.overstappen.nl/energie/stroomprijs/
Gas: https://www.overstappen.nl/energie/gasprijzen/
So apparently I slightly misremembered the prices; those graphs show that in 2020 the average gas price was about 84 cents per m3 (or about 8.4 cents per kWh assuming 10 kWh per m3), or 23 cents per kWh of electricity. That's closer to 1:3 than 1:4 on a per-kWh basis, but the general argument still holds that it seems like cooking on gas is cheaper than cooking on electricity.
I doubt most countries are as detailed as places I've lived in the US (Oregon, California, Washington) where I can look up exactly what type/% of resource was used to produce electricity.
Fingers crossed that this Russia debacle pushes Europe into a greener energy posture without much pain for its people over the next few years.
Your assumption that "the cost of transportation is approximately equal for gas and electricity" is probably not accurate, given that while the infrastructure costs are probably similar, the cost of the energy used in the compressors to pipe the gas around is likely quite a bit higher than transmission losses (around me at least, the service fees on the bill if you have gas were at least 50% higher than electricity last I heard).
You really don't want to be getting much of your heating from a gas stove (or unflued gas heater) not just because of the possibility of carbon monoxide formation, but because NOx and SOx produced by burning gas is actually a health risk (primarily asthma for kids, cardiovascular for adults).
I sincerely doubt this figure in cases where electricity is generated from fossil fuels in the first place.
For example, I lived in the Netherlands where 80% of electricity is still produced by fossil fuels, mostly in gas-fired power plants. As I understand it, generating electricity from gas has an efficiency of only about 50%. That means you lose a lot of energy before it even arrives in your home.
An electric kettle has an efficiency of about 80%, with gas stove around 40%. Assuming the cost of transportation is approximately equal for gas and electricity, that means using the gas stove is about as efficient as using the electric kettle, if you assume (most of) the electricity comes from a gas-fired plant.
In the winter, the gas stove will be more efficient since all the heat that doesn't go into your food, heats up the room (heating is typically also based on gas in the Netherlands, so this is basically free energy).
> Combined with passive cooking it could save real money
Again, I don't think this is true. Currently the energy market is fucked up because of the Ukraine war, but up to recently a cubic meter of gas cost around 1 euro, which produces roughly 10 kWh of energy, versus a kWh of electricity cost around 40 cents. That means that on a per-kWh basis, gas costs only a quarter of electricity. So even if the electric kettle is twice as efficient as the gas stove, it is still twice as expensive.
In countries where most electricity is generated by burning coal (like Poland, for example) there is also an environmental cost, since coal-fired plants emit more CO2 per joule than gas-fired plants.
YMMV based on local energy prices obviously, but I don't think it's straightforwardly true that electric kettles are always more efficient or more environmentally friendly than gas stoves, if you look at it holistically.