Doing so would be publishing non-representative data. Imagine an identified versus anonymous survey about cocaine usage in America. People will likely answer

Doing so would be publishing non-representative data. Imagine an identified versus anonymous survey about cocaine usage in America. People will likely answer honestly if it is anonymous. If it is identified, most people would be fine with it being identified and would mark no usage. People who do use cocaine would be more likely to not participate or lie on the answer.