Probably because sometimes a duke can have enough status for them to be called by titles like that? So like maybe that's why Viola goes by princess instead of wtv other titles there are
2 reason first english doesn't have the best term to design an high noble child
Second Duke daughter are princesses because when Duke's are related to the imperial family either by being cousin or brothers. Because their old title of prince is still given to their direct descendants
My gosh, the translation!
She’s the Duke’s daughter, so why is she introducing herself as a princess?
My eyes!!! (╯°Д °)╯╧╧