Plato misused the word "justice". He turns the arguments by Socrates in The Republic to make it seem as if the harmony of the state is based on a rigidly controlled caste system. It is rather a system of injustice and not justice or righteousness.
Plato's system is one where only the ruling meritocracy initiates the laws. This is enforced by a highly trained class of "assistants," who are the professional police and army. The rest must simply follow the trade or occupation of their fathers and mothers and are not allowed to do anything else. Indeed the educational system is such that there is no room for moves from one caste to another except among the Guardians and the Assistants.
This is sanctified by a lie that God moulded in the nature of various people gold, silver, or brass and iron. That is Guardians, Assistants, craftsmen or merchants. The slaves of course did not count, they formed another class like the untouchables in the old Hindu system of caste.
After seeing to it that, among the Guardians, the "best" men breed with the "best" women, the children are selected by the education system so that the "best" become capable of dialectic and a vision of "the good". These will be the future Guardians while the rest will be deemed only to have silver in their nature. As for those children of the craftsmen they will spend their childhood in the workshop or the counting house, serving an apprenticeship at the family craft or trade.
So the education system selects for and keeps in being a rigid caste system and people remain in the categories they are born in. This would obviously be distasteful to present day democratic thinking. However it has not been without its supporters in the past and the recent present. Hitler and Himmler, in the Third Reich tried to introduce a system of breeding and Hitler justified this in Mein Kampf in just the same way as Plato in The Republic. Francis Galton, a cousin of Darwin, also believed that people are genetically fitted to their station in life and founded the Eugenics movement.
Given that Plato's system is founded on a lie and that Hitler's breeding experiment ended disastrously it must be apparent that humans are far too complex to breed for single characteristics as one would animals. Anyway who can tell which characteristics in humans are the most valuable. Sometimes the most successful of men and women have been the most seriously flawed. In fact we all have our flaws of character and who can tell how breeding experiments may turn out since, though a certain trait may, possibly be enhanced in the offspring, while also exacerbating deep psychological flaws.
Even if you breed a pair of artists together you will not necessarily get a Picasso. You are just as likely to get a perfectly ordinary human being average in all things. On the other hand who can say what "ordinary" is when applied to people? Might not a loving concerned mother of children be of far more value than an Alexander or a Napoleon? Might not a jolly happy teacher or youth leader be of more value than a Caesar or a Plato? I think most of us would prefer a good and helpful neighbour than a prima donna of the soccer pitch to live near by.
We are mostly, all over the world governed by elites who send their children to those schools which get the best results in the narrow curriculum which they, themselves have devised or succeeded in. Yet which of us can truly tell which is the best way to teach the young and what are the subjects necessary for the good life?
Most educational systems are self-fulfilling prophecies which shut out the children or the poor or the underprivileged and keep them as a grumbling but subservient lower class. Nowhere but in a few private experiments has there been a true flowering of the talent that is latent in the working classes of the world. Sometimes men and women have clawed themselves up; "by their bootstraps" lifting themselves until they find their way out of the darkness of the cave into the glorious light of day and even get to see some vision of the good only to be driven back, by the haves to their "rightful " place among the have-nots.
Jonathan Rose, in his The Intellectual Life of the British Working Classes, gives hundreds of examples of people who have, from the most difficult and deprived of circumstances, managed to achieve excellence and, often outstanding success, in a variety of ways as well as in the public service. That many by dint of determination and sheer hard work did manage to do so suggests that there is a far greater pool of talent dormant there than few if any of the ruling classes have cared to admit or even to think.
