It can also increase your sense of community. By adding those who were interested in your story as close friends, you're gathering like - minded people around you. They are more likely to support and interact with you in a positive way. For example, if your story was about a local cause you care about, close friends added after might be more willing to get involved too.
One benefit is that it can strengthen your social bonds. After they see your story, they already have a fresh topic in mind related to it. This can make the initial conversation as close friends more interesting. For instance, if your story was about a new hobby, when you add them as close friends, you can immediately start chatting more about that hobby.