Why Fight Sadr?

Matthew Yglesias raises an interesting question:

"Is there any conceivable reason to believe that Muqtada al-Sadr is the greatest threat to the United States at the present moment? Is it not the case that his connections to America's primary enemies are, at best, tertiary (i.e., he gets some support from some elements in the Iranian government and some elements [possibly the same ones, possibly others] have sometimes turned a blind eye to al-Qaeda activities), and more likely provoked by the US campaign against him, than forestalled by it? If the answers are, as I think they are, "no," and "yes" respectively than why is the plurality of American national security resources currently dedicated to fighting him?"

I really haven't understood why we're going after Muqtada Sadr right now. He wasn't doing much except inciting opposition to the Allawi government, and the best way to counter that, I think, would be simply to make the Allawi government as effective as possible. When Sadr's charges against Allawi are that he's a puppet for the Americans who still rule the country, then sending the American military against him seems counter-productive. The general consensus seems to be that Sadr wouldn't win an election, so why not just keep trying to push the country toward that and then let him lose?