Because a god would more than likely get themselves killed trying to do it, and be obvious enough even they couldn't miss it besides. [Shun has minimal faith in the Heavens, but he's met enough people who know about the masks to know it'd be hard to miss.] It's a kind of curse that needs you to name an ayakashi. Considering the kind of blight people get from shinki who start to turn, naming a fully turned one would basically already be a death sentence for most gods.