But this assumes that the state is morally just by virtue of being represented by the majority.

Apart from the obvious real time corruption, that isn't taken into acount with this assumption, there are some other things wrong with this assumption.

It assumes first, that it is represented by the majority. Simply following the political process in America and analysing the make-up of the political class, we can see that the people in charge of the monopoly on force are not a cross section of the majority. It is a cross section of the upper class.

Secondly, why should the majority be right? This is called the fallacy of argumentum ad populum. It is not an argumentation for the legitimation itself.

So we clearly see that the monopoly is not in the interest of the people, and even if it were, that doesn't justify it in itself. The real justification is clearly not to represent the will of the people, because if it were, by nature of it being force, it would have forced its way into that position. Yet it is where it is: a monopoly controlled by the upper class, representing the interest of the upper class, maintaining the position of the upper class.

But the people still think it is morally just because they 'protect and serve'.