>>679022its hard to imagine the flame being on because you will imagine it being the size of the stove, which looks about half the width of the pot
but really imagine the length of the flame reaching out to hit the bottom of the pot,
it extends outwards pretty far - out the sides
this is a significant loss of energy
and you are blowing small numbers out of proportion too.
there is some truth about the circulation of the hot water being concentrated in one spot. yes technically this will make it heat slower but not nearly as much as you think.
if you took two different stoves, both outputting the same exact amount of BTUs and both cooking 1 gallon of water, but with different shaped flames, the stove with the wider pattern of flame will actually boil the water faster. but it will only be a 20 second difference. and this is for a gallon of water.
and also is assuming there is no heat loss from the wider flame escaping out the side. which it will