The Last Messenger was told how to reform the people via the revelation of the Qur'an. Some understood and put the message into practice whilst others rejected it.
Those that supported the Messenger were consulted about what needed to be done in the society and as such formed a 'government'; they made the decisions which were beneficial for all though there were some who did not like it.
Without a 'governing' class societies cannot function due to those who oppose the system and you will find in every society those who will oppose it, whether it be social justice or law and order etc.
Educating everyone with Qur'anic principles does not produce 100% perfect people and to live without police or the 'governing', you would have to remove free will from humanity; make then ants.
Just my thoughts on this topic and watch out for Sidqi Bhai!