Why would they make one?
The game will not be thrilling anymore if one can just build a shiny factory and do anything he wants with the bunch of shinies that he/she has produced using the shiny factory.
Besides, the game developers already gave you mushrooms to serve as sources of some shiny.
Although, not all players were given the opportunity to grow mushrooms on their yard, it depends on what country you live. Here in the Philippines, our yard doesn't reproduce mushrooms even if we play for almost a month.
Conclusion: Your yard is already a SHINY FACTORY, with the exception of those who lives in a country where mushrooms don't grow like in the Philippines, so don't even dream of having the capability of building another.