I don't think it would be too off color for artifacts to have an ability that made it more difficult to play enchantments. Something like an artifact version of Aura of Silence.
Obelisk of Silence

Artifact
Enchantments cost

more mana to play.

, pay X life, sacrifice Obelisk of Silence: Destroy All enchantments where X is the enchantments in play.
I think it has decent flavor, and a harsh cost. It would prevent welder from going crazy and just haveing a "tap welder: sacrifice an artifact in play to smash all the enchantments in play" sort of card. The card is balanced because It has several dis-synergies with itself. In that it makes it difficult for your opponent to get enchantments in play, but your oppoent could protect the enchantments in play by actually spending extra mana to play more enchantments. It has that clash of magic types flavor to it.
Edit, Perhaps this is slightly undercosted if your opponent only has 1 enchantment in play.
So maybe... Give them a "warning" turn. to drop some additional enchants in play to combat the Obelisk.
Obelisk of Silence II

Artifact
Comes into play tapped.
While Obelisk of Silence is untapped enchantments cost

more mana to play.

, sacrifice Obelisk of Silence,

: Destroy All enchantments where X is the enchantments in play.
I took out the pay life part mainly for looks, because it just had too many costs. :/