Initially, I planned that as well, but I decided against it, because it would make the golem more unique compared to others of its kind (similar to how the bearded devils and trumpet archons can channel their powers through weapons). If you believe it is better for them to just wield a weapon, though, I'll change it.

I'm currently working on pricing, and if it remains the way it is, this will add 10,000 gp to the construction cost.