well I dont think we actually leave a 'nature state.' what we consider justice is IMO just an evolution of herd or pack behavior, where we are banding together to protect ourselves from a threat, except that we are plentiful enough that we compete with eachother, and are wolves and sheep to eachother.
the strength of the tradition of herd protection from its own members, in our case depends on how much everyone agrees the killing of the scapegoat was warranted by an actual danger in the scapegoat. and how much we agree on that does have something to do with how dangerous the scapegoat actually was.
to support this tradition, the herd members need to 1. be in touch with the reality of whatever danger the victim represents, (at which point they will instinctively feel their right to end that danger) 2. believe in the herd or society's awareness of that same danger to be accurate and in agreement, 3. believe that the danger is substantive enough to warrant lethal force (ex. the danger itself is lethal or may cause severe irreperable damage such as mental damage), 4. believe in the herd's ability to execute the victim in the most surgical but efficient manner with minimal repercussions beyond the victim.
the sense of one's own right to live is based in instinct. the recognition of this instinct in others is the basis of society IMO. so without 1. the individual will not feel that it is rightful/necessary to support the tradition. without 2. then 4. would be impossible, but also without 2., even if 4. were the case, the individual would feel that the other individuals, the herd, were enforcing the tradition for unrightful/unnecessary reasons, and such use represents a threat because 1. not only makes the individual feel rightful in self defense by proxy, but by making sure the individual only supports the tradition rightfully, it let's the individual separate themself from the victim (and sometimes correctly) and thus disqualify themselves from becoming the next victim. so without 2. then the individual doesn't know that the individuals subject themselves to 1. and if they do not, they'd be qualifying themselves to be victims of the tradition. 1. operates on the basis of society, the assumption that all similar creatures have a similar right to live because they share a similar desire to live and have thus agreed to cooperate. the agreement, assumed though it may often be, is what grants the rights. the tradition of herd protection from herd member via lethal force, basically says that when someone breaks the agreement they render themself on the outside of the agreement, and the agreement-keepers are the society. specifically the victim breaks the agreement in such a way that forces someone to choose between their right to live, and the victim's right to live. It is considered part of the agreement that you dont force this choice on anyone. By forcing it you break the agreement and give up the rights the agreement gave you, at which point, all other things being equal, you have no right to live.
/tangent
3. is really just an extension of 1. and 4. is simply the recognition that if the herd can't protect an individual the individual can protect themselves. without 4 individuals will resort to direct self-defense.
tldr
you could simplify it to 1. you perceive yourself as being member of herd via agreement of society 2. you feel lethally or extremely endangered 3. you perceive that your feelings are shared or empathized with by herd 4. you perceive that herd is capable of ending endangerment better than yourself.
in the context where these criteria are met, it's likely your support for the tradition would continue as a natural social behavior, functioning as a combination of cooperation and self-defense. Your perceptions of these criteria will also be effected by whether reality echoes the criteria and how accurate your perception of reality is. As the realities of the individual, the victim, and the herd grow and expand, the perception of reality becomes more difficult and all the criteria are effected. the main reason I see today that the tradition has waned, is that the size of society by itself as well as the complexity of human behavior due to that size, has to some extent removed a logical understanding of what danger exists and how it works. people are less sure of both their safety and endangerment, and are thus less commited to traditions in general; because society is changing so rapidly, there is not a proper environment for old traditions to be modified appropriately or for new ones to form. Expect this to continue for as long technological progress is unchecked, or until societies learn to invest in cultural development simultaneously to other necessities, which would mean losing arms races.