I guess the purpose of flagging a post as duplicate is to prevent people from taking the effort to answer a question that has been answered before. So does it make sense to flag a question if someone has already answered it? Are there other reasons why a duplicate question should be flagged as such other than the one I've mentioned?
Yes. It does.
It helps to sort the site, it helps to point people to more answers, and it helps to signal that perhaps one should search the site before posting a question.