I think Touhou fan reality is that Shanghai is her daughter by now. When have you ever seen a doujin where she, for instance, blows up "a" Shanghai. Very, very few even have multiple Shanghais. Not to mention the cute Shanghai with magic baby little sister stories. But yeah, as the daughter of a goddess, she's a paradigm "lonely rich girl with dolls as her only friends" stereotype. She could move back to Shinki any time and be a princess at least in the Demon world.