Thermal capacity. Gas stoves are great because they have none, so any temperature changes are immediate. Anything between the pot and the flame will destroy that advantage.
Also, the combustion chamber will have a vent for the exhaust. So I would suspect that it won't be any more efficient, except for very small pot sizes.
When I got my first, I've been curious and experimented with water. Depending on the model they have sensor buttons where you can raise/lower the temperature in 10 to 20°C steps.
Mine have 10°C steps, where with water in a pot at 90°C the first few small bubbles start to rise, like in soda/mineral water. When at 100°C the big boiling bubbles start after about 2 to 3 seconds.
Mine are rated at 2500 Watts each, have segmented induction coils where the outer segments switch off with smaller pots, are plan like a mirror and thus very easy and fast to clean.
I'm such a fan! :-)
The airflow needs to be there, but I imagine it could be slowed down, so that the hot air spends more time transferring energy to the pot. That would retain the fast reaction time, and let one burn less gas for the same amount of cooking output.
Be that as it may, it's most likely more expensive. This is purely my personal guesstimate, but gas tends to be much cheaper in Poland than electricity. More efficient, maybe, but I'd be very surprised if it was cheaper given the prices.
On a related note, I was surprised when I did calculations on how much it actually costs us to bake our own bread. We started doing that a lot during this pandemic. It turns out, the cost of ingredients + electricity adds to slightly less than what it would cost to buy the same products from a bakery. This doesn't price in time spent on preparing and baking, but it's not like we could actually use that time to make money, we're having fun, and going to a store also takes time (and/or fuel). Electricity is cheap.
Speaking of which, I don't understand why we've settled on a gas stove design that's so terribly inefficient, with most[0] of the heat leaking around the pan. Why no design with a combustion chamber of some sorts?
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[0] - Well, at least a lot. I didn't do the math here yet, but it's hard to imagine otherwise with unrestricted airflow around the pan.