There are at least three reasons.
The first is that Jaafari’s presence at the head of a new interim government could deprive both Shiite and Sunni fundamentalists of their main claim that the new Iraqi leadership consists of a bunch of anti-religious personalities determined to reduce the role of Islam in Iraqi society.
The second reason why Jaafari was chosen is his good standing among Arab Sunnis who stayed away from the elections in large numbers.
I picked up a book in the library today, Imams and Emirs - State, Religion and Sects in Islam (1990) by Fuad I Khuri. It looks to be quite good, though it lacks an index which is not a good sign.
Jaafari also has the added advantage of having consistently opposed the policy of de-Baathification, so ardently advocated by his principal Shiite political rival Ahmad Chalabi. Hundreds of thousands of Iraqi civil servants, businessmen, and military personnel, who had carried Baath Party membership cards to remain in the game or even to stay alive, regard Jaafari as the only Shiite leader capable of preventing a witch-hunt against them.
Although the Shiites account for some 60 percent of Iraq’s population the total length of time in which they held the premiership amounted to no more than four years over a period of eight decades. Not surprisingly, almost all of Jaafari’s predecessors were known as “token Shiites”, brought under the limelight to help the Sunni-dominated regime negotiate a rough patch.
There is another, more important, difference between Jaafari and his predecessors as prime minister: They were all secular politicians. Jaafari, however, is the leader of the main wing of the Al-Daawah (The Call) Party, Iraq’s oldest political-religious organization. A glance at Al-Daawah’s memorandum of association could have a chilling effect on any reader concerned about the use of religion as a political ideology.
So, how concerned should supporters of democracy in Iraq be? Were those who claim that Iraq without a despot like Saddam Hussein is bound to fall into the hands of Khomeinist loonies right after all? Is Iraq to be transformed into a religious dictatorship under the Islamist slogan of: One man, one vote, once?
But here's a paragraph from the back cover which seems to have implications for the evolution of Iraq towards democracy:
Conflict and contradiction among Muslims centre around two poles: the ulama [imams], who derive their authority from religious dogma, and the emirs and sultans who base their authority on power and coercion. In Sunni Islam, for instance, the ulama's role is subsidiary to that of the power elites, but among the Shi'a it is the ulama themselves who form the power elites. After reviewing the ideological and organizational characteristics of individual sects, Khuri addresses the issue of religious change under the heading 'Brethren or Citizens'. Here, he deals with the interplay between religions, state and nationalism and discusses the contradictions between modern state structures and the Islamic umma [the Muslim community]. Already, he argues, some religious concepts are taking on nationalistic meanings.