Why would crime be reduced?
Most homicides are spur of the moment or based on some sort of preexisting emotional issue (cheating spouse/S.O, debt, perceived slight). A full 1/3 of the women who are murdered are killed by current/former partners. Only one murder in 7 is actually attributable to "criminal acts" outside of the killing itself, and that figure includes felony DUI.
What you WOULD get is a remarkable tit-for-tat involving close circles of friends or family members since that is the overwhelming source of murderers and murder victims.
Maybe, maybe not. A lot of what is being discussed is how things were in Appalachia in living memory. Feuds, conflicts etc. The key to resolving those was instilling a trust in local authorities, a difficult task in party controlled counties. Regardless, certain proprieties were observed, unlike the narco gangs today. The idea of a circle of tit for tat murders is dependent upon the circumstances of the killing, and whether the family involved (the victims) felt it was justified or not.