Not in the land of the free, Great Britain. You can put anything on your house, even a 25ft fibreglass shark diving into your loft.
https://www.headingtonshark.com/Home/About ("Hello. I'm Magnus Hanson-Heine, the home-owner of the Headington Shark House. The Shark House, formally titled Untitled 1986, consists of a 25ft-long fibreglass and steel shark crashing through the roof of an otherwise ordinary house on a quiet residential street in suburban Oxford...")
The shark scenario is more interesting, and was I'd say was largely allowed to stay because it was an art installation. They couldn't have built an extension of the same proportions without planning permission.