A large part of the problem and solution relies on the field we're talking about. There are law forums, but unfortunately, the law is incredibly specific and varies wildly from jurisdiction to jurisdiction. There would have to be a LawOverflow for every county. Medicine is incredibly situational as well, and that doesn't include the doctor patient confidentiality clause, which means the doctor needs permissions even to ask general questions. Now, if you were talking about students, then the style still wouldn't work, because the answers are in the textbooks, not in other people. Cars and home improvements have the best chance, but as was mentioned, The people answering the questions have to be spending a lot of time at the computer, rather than spending their doing work on cars, or doing construction work on a house.

The reason StackOverflow works is that computers work based on their code, and so a certain compiler will interpret C# code in a certain predictable way, so the people answering the questions don't have to be anywhere near you. And they are able to answer in a relevant way. The same is not true for other fields.