While I'm sure everyone would like more pet food in the same way that everyone would like more diamonds, I can't really see it happening. When the feeding animals first rolled out, Inno said that scarcity of pet food was a limiting factor for the powerful feeding abilities that these buildings had.
If pet food were as plentiful as mana or seeds, then the "limiting factor" of having to decide when you feed your pets goes away and you might as well make those benefits permanent.
Having a building that produced pet food, even at a rate of 1/week (unless it was a unique building that you couldn't have more than one of) would completely wreck that balance. It would also threaten to become another one of those "required buildings that everyone must have or you are hopelessly behind everyone else" like the Fire Phoenix has become.
[Maybe an expiring building, like the Trading Station, would fly. 1 food/48 h, expires in 50 days. But even then, Inno would have to make it rare enough that you couldn't just flood your city with them -- like one of the rare chest prizes in the spire.]