The trick here is you want to control resonance in the arm wand, such that it does not talk back or editorialize.
Most wood arm wands I have seen do not appear to be treated for resonance issues. Some might argue that they don't need that; they would be wrong. The better metal arm wands are indeed treated- less expensive ones are not and so seem to have more coloration.
Resonance is not the only issue. Effective mass with the cartridge also plays a role, which is part of mechanical resonance which is a different issue. I point this out to reduce confusion.
A metal arm wand can improve shielding, which may result in lower noise.
Here in Minnesota there can be another concern- humidity, which will not affect a metal arm wand, but will certainly affect a wooden one! I'd hate to have an expensive arm wand crack in dry humidity, or have it change dimension or warp. That seems like a problem not worth having to me.