The establishment of an International Criminal Court was motivated by the growth of impunity during the late eighties and beyond when state power was contested by armies and armed opposition forces causing unrestrained brutality that outraged the human conscience. The butchery of human beings by those in power and those who sought to remove them by force in the absence of credible law enforcement and judicial system motivated many to support the externalization of the justice system so that impunity would not prevail.
This notion of combatting oppression is different from the externalization of justice to combat common criminality. Crime in many countries with poor leadership is motivated by dysfunctional states which put people in prison without rehabilitating them to come out to live useful lives. Hence instead of combatting crime, they end up building an army of recidivists who come in and out of prison without stop. Instead of building prisons, they build concentration camps.
Hence externalization of such criminal justice system does not add value in the promotion of justice. The states only collaborate to hunt common criminals without doing anything to rehabilitate them and save them from the world of criminality. While establishing external judicial systems to combat violation of rights and curbing impunity in a dysfunctional state is worth promoting, the best way to fight common criminality is to build a state that would be ready to make each youth to have gainful means of existence.
Hence only a few would need extra measures to be rehabilitated to live normal lives.