Gingerbread people are bestowed life by magical bakers. The same magic could be used to bring a gingerbread house to life it just would be in a nightmarish situation since houses don't have many moving parts besides doors and shutters. Most magical bakers would never do something like that because magical bakers are bestowed their powers by the love of the people they feed. People who find joy in feeding others are rarely ever evil and therefore would never create a nightmarish monster gingerbread house.
His fans are some of the most grotesque creeps you could ever imagine. They see themselves in him. Just like any other group they love to see themselves represented among the wealthy.