Actually the original quote is "the plural of anecdote is data". As a scientist, I support the original. All scientific observations start as anecdote.
It's impossible to eliminate bias. Whenever you report a measurement, the answer to "why did you choose to measure that particular thing to represent the phenomena" implicitly encodes a set of biases, and a tower of biases that a lot of other accessory things are built on (why did you use that instrument? Why does that instrument use mechanism X and not mechanism Y? Why do you use filter Z when processing your data? Why did you use exposure time T for the imaging, why did you pick that particular P-value threshold, etc.) these are all at some point, subjective judgements. Biases are not a priori bad
Bias is unavoidable, but definitely reducable. Biases are the least harmful when they are well understood. The problem with just haphazardly collecting anecdotes is that the biases tend to be poorly understood becuase the collection protocol is inconsistent and poorly documented.