Then give it the Super Smash Bro ability that adds 1d10 damage to the weapon used, or give it Smush the Enemy, which allows it to double it's damage 3 times a day. Or whatever ability you want to bring it up to the CR you need it to be.
Just allowing it to do X damage with any weapon you arm it with just because it's a hobgoblin does both the hobgoblin and the weapons a disservice. Both should have meaning independently.
It's a mage, not a wizard.
Seriously, though, there are hundreds, perhaps thousands of different "classes" and "subclasses" out in the wide, wide D&D world. The WotC is allergic to give us players more options doesn't change that, so if the mage is a bit different than a wizard as a class, that's not unusual. A mage picking up a dagger or a greatsword and hitting for the same damage would be.