I would rephrase your statement "the problem with anecdotal evidence..." to "a common problem with anecdotal evidence...". As I see it, and increasingly see it, people are told that their anecdotal experience carries little value. I think that in reality an intelligent individual can extract huge swaths of truth from anecdotal evidence. The backlash against that kind of thinking is really a form of thought suppression and brainwashing. We are told that speaking in generalities, stereotypes, etc is dangerous and flawed. This type of thinking falls under, in some ways, a political effort to people stop from coming to their own conclusions about why people act the way they do. Its along the same line of forcing politically correct speech.

The caveat here is that real hard science needs real hard data, not anecdotal evidence.