Should totally be a thing.
Even if it's just a few baseline class-specific passive effects that change based on what kind of weapon you're using.
Axes, swords, and maces used to have talents for warriors.
I think it'd be neat to do all weapons at once.
Maybe something simple like just each weapon type being tied to an existing talent, granting you access to it while youre wielding that weapon without having to spend a point on it.
It'd be nice to have a reason to choose a specific weapon type instead of just plain stats