The English originally started with manorial courts and clerical courts, the former as a court of first instance for some things that would never see an assize or quarter sessions or reach the sheriff’s eye, the latter running a separate but publicly sanctioned set of law, courts and punishment. Arguably, the church courts were actually an intrusion of a system of international law/foreign courts into the English system. Not for nothing the RCC has been compared to the UN/ICC/EU. The manorial courts were privatization of first tier justice at least insofar as the lord of the manor was not exactly operating as a public officer in that system. [YMMV on the nature of Norman England and public v private, I suppose.] There was also guild justice and other semi-private systems in the towns, although the public/private amalgam was arguably stronger.

Some of those lasted many centuries as the modern Common law and equity courts evolved. Modern Anglo societies have continued to allow all manner of private justice at least in civil matters, on a contractual or customary basis. From every corporate arbiter for hire to rabbinical and sharia courts, or whatever Amish and Mennonite self-government involves.

Of course, they all have potential for abuse and it’s well worth the effort to make it clear that their scope is limited and to find ways to let members of communities know they have an out if they are even willing to take it. That last is a perennial problem.

That and never let such courts claim criminal jurisdiction or impose penal sentences. Jesus.