From my point of view the concept of a "battlemage" is a spellcaster or hybrid fighter/mage who can perform equally well in melee combat. So it sounds reasonable enough to me if the "default" weapon of a battlemage is an axe, for example. Of course, his skill set should support that particular combat style, as well.
I remember in Dragon Age: Inquisition there is a unique staff that looks like a greatsword with a greatsword's moveset. It's the only melee staff that functions as both a spellcasting tool and a greatsword. I used it with my knight enchanter character and I think it worked perfectly with the concept of that class - a melee bruiser/mage. I love odd-one-out items which fit specific play styles like that.
