Is Building The City Helpful For A Definition Of Justice?

I would say no. In saying so I do understand why Socrates is creating a test-group society. Test-groups are helpful in finding answers, as long as those test groups are representational. From my understanding Socrates is searching for a definition of justice in how it is present in the world. Justice being present in the world will only be found within the real, natural flow of the world. In restricting the city from acting in such a way as a normal city would, and shielding its citizens from such things that any other city in the world have access to, will not result in an accurate portrayal of justice in the world.

Different factors will affect the definition in a society where certain things are withheld as opposed to one with more freedoms. For example, if there is no laughter what will citizens do to act out these goofy and endorphin-filled releases? If glamour is taken out of certain jobs, i have a hard time believing that there will not naturally fall a distinct rank of glamorous jobs and those less glamorous. I don't trust that women won't naturally go after gold-metal souls, and in such, create a desire for that type. Women chasing this type would create a desire for non-warrior born souls to strive to be that. Beings are selfish, and I feel a number of beings stuck doing what's "best for the city", but not themselves wanting to do it will create a problem for the city in the long run. Possibly a social uprising from lack of freedoms and unhappy citizens.

Also, what if a warrior has a moral issue with murder and violence? Forcing someone to kill...is that just? Unwillingness to hear opposition from any citizen unhappy with their job, so long as it benefits the city...is that just?

Again, I would say no.