Courts that just willy nilly convict obviously innocent people would not only not get very far, they would be subject to legal action by more upstanding courts.
Who is the judge of that? The free market, i.e., the court that gets the most support (i.e., that brings in the most business) is presumed to be the most "upstanding"? That would be like suggesting that the restaurants and food brands that do the most business are the ones that have the highest-quality food, when in fact the ones that rake in the most money tend to be the ones that willy-nilly destroy the health of their customers.
What's to stop private courts from doing to justice what Monsanto and McDonalds do to food, and getting away with it in much the same way, i.e., by outspending their detractors?