Ciri did the witcher trainings but didn’t undergo the mutations so she wouldn’t be able to use elixirs and wouldn’t have the usual witcher benefits. Also, the mutations would kill her because she’s a girl, so they can’t implement that. And her fate after The Witcher 3 depends on a playthrough so it might prove difficult to continue, unless they just make one of the endings the official one.

As fun as it would be to play any class in the world of the Witcher, I think the protagonist should be a witcher to fully focus on witcher builds etc. for the game to stand out from other fantasy RPGs. Perhaps they could introduce different witcher schools to choose/develop. But since the game will include Geralt, I sense he’ll be our trainer and hence it will the school of the wolf. Let’s wait and see.