Sometimes, this is completely appropriate, as when someone is using an anecdote as their only support in a vigorous debate, or when information is clearly being presented as factual, when it probably isn't. But as "Citation Needed" has become a rampant meme in its own right, I think it is increasingly applied in knee-jerk, cargo-cultish, and inappropriate ways.
Sharing anecdotes and experiences is one of the fundamental ways that humans share information about the myriad little nooks of the world that we move through. I know it isn't science. I'm quite well read on cognitive biases, statistics, and the scientific method; and I do not need to be reminded about these by HN commenters continually, every time somebody shares a story, or an opinion based on their experience.
I'm concerned about a chilling effect on the sharing of anecdotal information. There is information - information that I can use - in the many experiences related by others. I don't need or desire to get fully 100% of my information from peer-reviewed scientific studies. I know the difference between science and personal experience, and I would much rather bear the burden of telling the difference for myself, as the reader, than to have fewer people talking about their personal experiences.