With litigation issues they don't get private, because every one can go to the court and will have knowledge of the dispute resolution process.
It is not always quicker also, it sometimes could take even more than a year before there will be a ruling over the dispute by the court. Mostly appealing to the court by both parties makes the resolution longer.
It is costly also, in terms of both time and money, a lawyer will have to be hired if the firm or individual doesn't have one and up and down transportation to and fro the court is all costly.