You would prefer that this prison contain an infinite number of Cloud Strifes who have all done the exact same things?
It is unreasonable to suggest that this system should capture every iteration of the same person. A particular individual in a particular timeline is selected for the lottery, which is random, and then they are put on trial. If they are found innocent, nothing happens. If they are found guilty, they are incarcerated. There is a prohibition on trying criminals who have already been arrested unless their timeline has a significant deviation from the existing criminal.
You think of it is as "one unlucky iteration who is punished for their crimes", but instead, consider it "one lucky timeline that has that iteration's crimes corrected, thus improving it as a whole".