Fun little explanation as to why this happens on some items:
Items essentially have code on them that runs when a different item is used on them.
If an item doesn't have any code assigned to it it'll run the default code which includes checks for notepaper functionality etc.
Other items that do have their own unique code can then return back to the default code after (this is what we see on things like herbs that can have potions/incense used on them but then also work with notepaper)
In the case of the wizard hat, it has its own unique code for working with black ink but then doesn't return to the default case.
We could realistically fix the majority of these notepaper issues - it'd just take some time to find them all.