The "court" is a metaphor, like the "marketplace." As such it has no power to actually make policy. That is for elected officials.

What it ought to do is inform the body politic. Take your climate change example. The "courtroom of ideas" wouldn't just establish that climate change is happening, and driven by human activity. It could also help settle some questions about the relative costs and efficaciousness of various proposed policies. Those discussions would be valuable to voters who want to select between politicians based on which policies they support.