There's definitely an Imperial Court, the main character of Arena was a member of it.
Skyrim having that kind of judicial system just seems...inappropriate.
To have courts, I don't think it's inappropriate (not fully). I wouldn't want courts to be like our modern courts, but more like... well. A judge, simply. Nothing more, nothing less.
Solving disputes by a neutral, judicial part has existed for thousands of years. Skyrim is civilized too (moderately). Bigger cities could have some kind of court. And the Nords aren't too far off from Imperials in that sense I think...
The only reason it could be inappropriate in Skyrim now, would be because of the civil war. Courts basically seize to function without its support of the system of law.