cherrybim: If the reason for Reb Moshe’s heter is “extinguishing without a wick is not kibuyi”, would it be permitted to turn off a gas burner or electric light on Shabbos as well??? If there is no melacha of kibuyi involved, why not? “
Probably because the melacha of cooking is ONLY permissible on Yom Tov (and is therefore referred to not as melacha, but as meleches avoda, and that is the only reason the use of the stove is permitted. It’s totally and unquestionably assur to use a fire for cooking on Shabbos, so the inyan of kibui is irrelevant also. If the cooking is the issue at hand, then the kibui is secondary to that. If cooking were not one of the L”T melachos, it takeh might be a different idea.