I wonder if any states have built a governor's mansion in the last fifty years. Massachusetts does not have one, and I consider that a symbol of the stupid Yankee frugality that manifests itself in this oh so liberal state. A governor's mansion helps to emphasize the public role that the highest elected official has in the community. Critical social functions, including fundraising, can take place there and will be more open to the public eye than if the governor has a more private residence.
I'm not sure what forces would have to align to build a governor's house in this day and age. I wonder if the forces of tradition would triumph over the forces of modernism. Probably.