I believe you don't have this problem with stackoverflow because it's user generated content. Answers provided by people doing it out of passion are usually better. That's why you'll often find the best answers on Reddit.
As to why there is no successful medical overflow.com: Software developers are inherently more web-affine and likely to help there. On top of that it's a great way for developers to show their knowledge in a way they can show to prospective employers. The medical field is a lot more old-school sand I cannot imagine a doctor showing their online help history to a potential employer.
The difference is that software developers have a freedom of speech online. There is no legal liability or professional consequences for a junior coder accidentally giving out wrong-headed or misleading programming advice. So coders post freely, and the good posts eventually float to the top.
In licensed and regulated fields - law, medicine, finance - the situation is quite different. Posting a bad answer might result in you getting sued by an angry reader or investigated by your field's regulatory body.
As to why there is no successful medical overflow.com: Software developers are inherently more web-affine and likely to help there. On top of that it's a great way for developers to show their knowledge in a way they can show to prospective employers. The medical field is a lot more old-school sand I cannot imagine a doctor showing their online help history to a potential employer.