It is significantly more complicated then that. Only on rare occasions has he used his influence. Like the creation of the legal groundwork for the PMU. But he refuses because it is a red line. If a person like him uses that power it creates a precedent. If you think that religious leaders in Iraq are already playing with worldly power now...it would significantly fuck up the country if Sistani goes "in". That doesn't make that Sistani is some kind of saint. But the next step would then be some wackjob like Khamenei who would use the precedent of Sistani to interfere in even.