I think it's important to take note of the fact that there are many, many "criminal justice systems" operating within any given kind of society. It happens any time people enact judgment on another person, in a sense. The real question is about legitimacy in my mind, which is more specifically to say how well the system of justice is matched with the society it serves (I vaguely remember some maniac raving about this at length in a few of the more aged "ethics" threads on here). "The People's Court" is exactly that. You are trying to endorse the values of the majority of the society (with force hopefully taking a back seat in that endeavor). That is the real meaning a "justice" system carries for me. The Salem witch trials were a legitimate expression of that society's values as far as I can understand them (even though the solidity of their reasoning might have been questionable from my point of view), and so were "just" in that arena. I truly don't believe altruism exists, so to start breathing fire about how one person takes advantage of another and how this or that situation is unfair seems kind of pointless to me, or is at least belaboring the obvious (which is probably a better way to state it). Justice is not a "personal" or "forensic" concept to me. Vox populi, vox Dei. [You are acquitted, Captain Crocker.]
One thing I've noticed is that formal affairs are often generated out of informal ones through what I would consider a completely natural process. I'm probably not the person you want to talk with about the history of law, but I'm sure the judicial system we have now didn't just spring out of the ground. Necessity is the mother of invention, as they say. The thing some people don't seem to realize is that... it's a completely natural process. It doesn't stop. The real "Charles Bronson" (or some literary equivalent) situations aren't coming out of nowhere; those circumstances are (often admittedly) an informal reflection of a developing failure (and a need) within a system like any other, which is perhaps simply a failure of the system to adapt rapidly enough to the demands of the society (for whatever reason, and perhaps a large part of that responsibility lies with the criminals themselves) or much more seriously, as a disregard for the demands of the society. What I see that bothers me, and have gotten better at seeing, is when people try to use those realizations as a vehicle for notarizing their conduct in "personal matters". It's the same kind of mechanism as "we're doing it for the children", and a bold variety of hypocrisy.