mitoch - machlokes Bavli and Yerushalmi?

The Mishna in Beitza (12) records the famous machlokes Bais Shamai and Bais Hillel regarding the principle of “mitoch”. According to Bais Hillel, once the Torah permitted cooking food on Yom Tov, all acts of cooking and transferring fire are permitted. The gemara goes so far as to say that if a person cooked basar b’chalav on Yom Tov he would not be punished for breaking Yom Tov even though the food is inedible. Yet, the Yerushalmi (Beitzah 3b in Vilna ed) writes that there is a machlokes R’ Yochanan and Reish Lakish whether someone who cooks neveilah on Yom Tov would get malkos. Question: Why would we not apply mitoch to this case? I find it very hard to say that R”Y and R”L did not learn the Mishna as an issue of mitoch (though some Amoraim in the Bavli do try such an approach). Perhaps the Yerushalmi holds that the cooking, even if not for the sake of food, must still serve some need (similar to Tosfos’ sevara in explaining mitoch), which neveilah does not. Any other ideas?