Way-out

The reason of making Li Shiji the prime minister was simple: It was his honorable way out.

You know, when Li Zhi (李治) became the Tang Emperor after the death of Li Shimin (李世民), miliary campaigns against the surrounding tribes were largely complete, and the central Tang government planned to take over the control of the army from individual generals. Li Shiji was a major target because he was leading a gigantic troop, and his personal relation with Li Zhi was not entirely satisfactory.

For that reason, shortly before the death of Li Shimin, our Emperor Taizong advised his son to appoint Li Shiji as the chief of the government - a brilliant strategic move. The famous general would have to give up his army and be literally promoted to an irresistible honored position, the work for which was onerous and unfamiliar. He would not think of uprising because he had no good reason (and Li Shiji seemed to be naive enough and believed the Emperor was really promoting him).

The result? Li Shiji stayed in office for just over a year - and the rest is history.

PS. You may not find this story in the traditional Old Book of Tang (舊唐書) or New Book of Tang (新唐書). Well, there is. Just read between the lines.