The format looks neat and I'm sure it could be of some help. But it's also very limited, as it can only express some restricted uncertainty withing the format of the date representation.

There's no qualification about the range of approximation. For example, "a day in May" may be restricted that it was definitely before the 14th of May. So the uncertainty could be narrowed down to between 05-01 and 05-13. And there's no way to express unspecifics that relate to properties not represented in the format, such as "a Tuesday in Dezember" or "a day in the second week of March".

So, I believe this extension is probably not very useful unless there is a practical use cases where the described methods of expressing uncertainty would be completely sufficient. That's highly unlikely, because uncertainty typically has soo many different angles.