What we know, as Nynaeve demonstrated, is that trying to remove the effects of Compulsion using the Power is tricky and can damage the victim.

We don't know if simply nullifying the weave would have the same effect. I would say that the best way to test this would be to send the victim of Compulsion into a stedding to see if the weave was effected. That would imply the effect was from a tied off web (which seems to be the case given the evidence Nynaeve found).

Regardless, the question this brings up has more to do with the scene: Why bother removing the Compulsion from Elza at all? The nature of her self justification made her want to do anything necessary to see Rand go to the Last Battle so he could be defeated by the Dark One. It wouldn't have interfered with freeing Semirhage and removing the wards since those actions are direct ways to accomplish the goal.

I think this scene is noteworthy for what it reveals of Shaidar Harans' limitations and less so because of how the weaves' effects were dealt with.