True, but having the goverment show that it can protect the interests of the Shia weakens Mookie's hand: his support is based on the perception that the goverment can't protect Shi'ite interests.
This symbolically shows the government can undo something the US did that was harming (in a prosaic, grid-lock inducing sort of way) the residents of Shi'ite neighborhoods of Baghdad.
Our boys will still be hunting for the kidnappers, and if we get lucky will catch Mookie himself in a firefight, we just won't be snarling traffic as a tactic for doing it.