What efficiency (in terms of energy transfer to the intended material vs to the environment) is observed with gas? IIRC, gas achieves maybe 35-50% efficiency (depending on the surface area and material of the pan) compared with ~80% for electric resistance heating and >90% for induction.
Adam Ragusea did a water boiling comparison and the gas stove was dumping so much energy into the air around the pot that his thermometer melted [0]. I just don't see how any pan geometry could extract much of the energy from the quickly rising hot gas produced by combustion.