I tend to think it’s more a holdover from when arbitration and law was not standardized and had no oversight. In a situation where your legal arbitration comes from layman of the law or laymen of the church, the oversight and commonality of the church/faith was the equalizer.
Now, application of the law has oversight. Those who practice it go to various schools to learn how to apply it evenly and universally, and everybody offers their advice and services based off of the commonality of standardized practices.
The other thing that exists now that didn’t exist then… Democracy. The Bible is full of cautionary tales in what happens when one relies on the powers that be (royalty, appointed officials, those who seize power through conflict) for arbitration. When that is your judicial structure, then relying on internal modes of justice just makes more sense.
But these days? Nobody says (or should say) they’d rely on a church for legal resolutions. There is no standardization in the church that meets the level of universality that the legal system we have now. And, most importantly, the law overrides the ruling of the church. What the church decides has to be supported by law and, if it’s not, it’s void. So having a lawsuit settled there is non binding and, in the case of financial payouts and restitution, it likely won’t be accepted by third parties.
If I get into a car accident and sue the person who hit me for injuries and I say to my insurance company “don’t sweat it, we worked out payments and restitution via the church legal system so it’s settled,” they’ll say “that’s cute, tell them we’ll see them in court.” Or they’ll say “cool, but now we are dumping your coverage because you’re not supposed to take deals without going through us.”