ROB: Check the sources I brought on the first page. The Gemorra Beitza 22 writes that one may not extinguish a fire to save ones house from burning down on Yom Tov and this is brought in Shulchan Aruch 514:1. I don’t know about real estate values in the time of Chazal and I am aware that oil prices are on the rise, but I think it’s safe to assume that it is clear from the Gemmora that turning off the burner to save money on your gas bill would NOT be grounds for a heter on YT. Unless you consider the Gemorra and Shulchan Aruch to be unnecessary machmirim.
This Halacha is clear by itself that we do not say “mitoch” on kibuy. For a reason see Mishna Berura 518:1 where he explains that “mitoch” only applies to a melacha that is PRIMARILY ochel nefesh such as cooking. Extinguishing is NOT.
My comment on the “political points” is that you try to reduce a discussion in Halacha to a philosophical debate on chumros vs kulos. Nothing could be further from the truth. I fully agree that koach d’hetera adif, but when there are NO grounds to permit something we have no choice but to rule assur. This is clearly the situation at the case in point.
One thing I will concede is that if you want to turn down a pot to simmer and the ideal temperature to do this can be generated by the pilot light alone, there would be grounds to permit this. However I don’t believe this is the case.