Would the mullahs prefer the US iced Sadr and saved them the trouble?

It is my understanding that there is no love lost between Muqtada al-Sadr and the other Iraqi Shi’ite mullahs. They consider him a punk and an upstart who would be drunk in a Texas bar if it weren’t for his daddy — wait, I’m mixing him up with somebody else — drinking bootleg hooch in a Al-Najaf coffeehouse if it weren’t for his daddy. But he has a lot of noisy, violent followers so the mullahs can’t whack him without endangering themselves. I assume they are real pleased he’s pissed off the US because we seem to be happy to do their dirty work for them and if it triggered a civil war who’d notice?

Is my assessment accurate? Or do the mullahs really want Sadr to live a long and troublesome life?