> This is about three times as energy-efficient as a gas hob.
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.