There are so many holes in this logic I don't know where to start.
First of all, the assumption that justice makes one content; what is the basis for this belief? Is it not equally possible that a man who acts in the name of justice will become bitter and resentful over never being appreciated for his good deeds, while his counterpart prospers on the suffering of others? How happy any given individual is with any given situation depends entirely on them and who they are; psychopaths, for instance, are defined by a lack of remorse or empathy.
Someone who cares about nobody except themselves (And make no mistake, such people certainly exist) may be completely satisfied with a life of riches gained at the expense of others. Plato is simply projecting his moral instincts onto others.
And I haven't even began to talk about the concept of objective morality.
Consider the atomic bomb dropped on Japan by the United States during World War II, an event that took the lives of countless innocents, but who some would also argue was for the greater good. Some say that Japan would never have surrendered otherwise, and that an equal number of people would have died in the coming long and bloody war.
Whether or not this argument has merit, the situation is almost certainly not unique. If injustice is itself a sort of "ingredient" of justice, then can we still call the result justice? Would a just man then feel no guilt at the mounds of corpses left in his wake, so long as it was in service of a "Just" result? If he doesn't feel guilt, and argues that his actions, while harsh, were in the service of justice, then what objective standard would we measure him against?
On the other side of the coin, perhaps being unwilling to compromise ones morals for the sake of humanity as a whole is equally reprehensible. What of the man who refuses to ever take the life of another, even when doing so would save the life of an innocent? If his choice knowingly results in the spill of innocent blood, does the simple fact that he did not commit the murder with his own hands excuse him from allowing it to happen?
Ask yourself this; if humans were without empathy by instinct, how different would our standards of morality be? Something is "Objective" when it is without bias, not influenced personal feelings. Thus, a logical and objective system of morality would be an inarguable standard of value, that was self evident and complete, and anyone who said otherwise would do so only due to a lack of insight on their own part.
But "Value" isn't on the fucking elemental chart; it's an entirely mental activity. One could not judge something to be valuable or not valuable unless one was able to distinguish between objects, otherwise everything would be "good" or everything would be "bad", and by virtue of being separate from the object you are judging, your perspective is a subjective one; it is unique to you.
The fact that one person may see value in something and another might not proves that value is something that can be projected and manifested by the mind. Even if we were to imagine that some magical objective version of value existed inherent in objects, that we were simply incapable of seeing, the question then becomes what purpose such a thing would serve.
If the existence of this "Magical Value" had impacted us thus far, then our reason for taking note of it would be one of necessity; it would have a practical benefit divorced from any conception of right and wrong. If it had not affected us, then it's existence would be almost irrelevant; the lives and actions of those who took note of it would be no different than those who did not.
Any given individual's conception of justice can take almost any form, and if that is the only standard you hold them to, then you are permitting them to do ANYTHING THEY WANT.
For the record: If I had an invisible ring, I would do fuck all; it wouldn't be that useful. If I could truly act without consequence, however, then I would rob Donald Trump blind and use all of his money to take over a big game publishing firm like EA, then fire all the board members (I'd keep them around as middle management, to help me run the business) and start my own design studio to make my games. Then I'd spend all the rest of the money on funding green energy, science projects, and space programs.