Tosafos adds that because he can find no other way for a house to affect food or eating. The eating part is no doubt added in. He could have just as well said ??? ???? ??? ???? without the eating part. And it’s not like Mitoch has to translate back to food, since we find in Beitza 12 that it applies to Tiyul and for the sake of a Mitzvah.
I guess I don’t have a rock solid case but not do I think we start building ????s from any possibility of Hetter. The ???? by ????? is not was you think of when you learn of ???? nor when you think of food preparation. It is a specific crossing point that between ???? and ???? ???. It would be more ????? to Assur cheese making — since ???? is not a food ????? — than it is to build a Hetter out of an exception.