It seems inherently fair to our animal instincts that a victim of violence should received "satisfaction" for their unjust suffering. But do the victims gain anything from this supposed satisfaction? Maybe some of them do experience a reduction in their ongoing suffering; I doubt it makes the pain of loss go away entirely for most.
But more importantly, how does the system of retributive justice impact society beyond the perpetrators and victims? I would argue that its impact is almost entirely negative. The perpetrators are themselves repeatedly victimized, often disproportionately to their original crimes - by the general dehumanization of jailing, violence at the hands of other prisoners and guards, social humiliation and pariahdom, economic and political disenfranchisement. But their victimizations are largely considered just and legal, and thus they cannot redress their grievances through the law. So what do they do? Leave jail wounded, aggrieved and with further criminal training, even more likely to commit crimes (and worse ones at that) than when they went in. Thus they create more victims, and the cycle of suffering is perpetuated and amplified.