Especially in a field with high risk of data being abused by ill-intentioned people such as "vaccine and autism" link, it would really surprise me that everyone just kept happily the 95% confidence, and didn't aim for much higher confidence.

Okay. Be surprised. It appears that I've read hundreds of medical journal articles and you haven't.

Medicine isn't like physics. The data is incredibly messy. High sigma results are often unattainable even for things you know are true.