"Minarchy" still creates two classes of citizens: ordinary people like me and you, and "special" individuals who get powers that ordinary people don't have. In today's society they are the police, the judges, the politicians, and other bureaucrats. The only different is where the line is drawn in terms of defining the size of government.
Any system that gives power to a subset of the population will eventually fall prey to corruption.
This is true. So to minimize the system minimizes the potential damage caused by that corruption.
It's important to realize that there will be no perfect system. This is the mistake the statists make. Things will be perfect with just-a-little-bit more government. They accuse libertarian and like-minded people of being Utopianists but that is far from the truth, we merely want to move towards "as good as possible", not "perfect".