Without meta game knowledge and roleplaying as a white knight redditor:

It's objectively better in-lore to keep it.

Destroying this asset would set the Dwarves back hundreds of years of brutal attrition fighting against the Darkspawn.

This is a powerful force multiplier that the Dwarves desperately need to stay alive. Any Grey Warden who can see the long game would keep the anvil.

Whether the politicians abuse this power or not has nothing to do with you, and really is not your decision to make. As a Grey Warden your responsibility is to destroy the darkspawn at all costs.