oomis: Thank you very much for reading my posts and responding to the points I bring. Certainly it is true that one may not cook an a fire on Shabbos, but one could leave say a pot of chulent on the blech. According to cherrybim that there is no kibuyi w/o a wick, why couldn’t one turn off the gas fire after serving the chulent? The issue of bishul is irrelevant, it is only an issur of kibuyi. Also, according to his position, why not turn off electric lights or heaters, as they also have no wick? Of course the obvious answer is that kibuyi is 100% relevant even w/o a wick, however it may be derabannan because of melacha sheina tzricha l’gufa.
Your point about muktza is excellent. Reb Moshe actually writes that one may not adjust the pins on a Shabbos clock because of muktza, and presumably the same may apply to the knobs of a stove. Since YT is even stricter then Shabbos regarding muktza, this would be an additional reason why it is forbidden to turn off the stove on YT when not for ochel nefesh purposes.