On a personal level, justice might just be to 'right the wrongs', with no specifications on how or why or anything, so as to incorporate the wide range of opinions and feelings people have
But justice is also used in the context of law (which is that without L seems to be implicitly talking about). If completely rational people were to sit down to create a system of law in society, disregarding what people think should be part of that system, they would still most probably 'use' the idea of justice. Purely in service of creating a better societal system.
And that will only be because they'll see that justice helps prevent further wrongdoings.
So in a sense that is the only reason for it's existence in our society, otherwise when people were constructing all the modern societal systems they might have chosen to discard it/would've been discarded later. (ofc imagining the creators of the modern societal systems as purely rational isn't quite right; in reality you should see this example more as "it doesn't matter how or why those specific people chose to include justice, but even if a purely rational agent was substituted in their place, it should've reached the same conclusion")
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