Great idea! As I understand, you suggest that the user would choose certain close people for the app to "manage" communication with? What if the app did this on its own by simply tracking your communication level with various contacts?
Obviously, those people that you communicate most often with are those closest to you at this period of your life. So the app could "bug" you to reach out to them once there has been no communication with a certain close contact for a while.
But what's perhaps even more important is that this way the app could identify long-lost connections and try to retrieve them. It would scan your old chats and identify once quality connections that were lost and from time to time display pictures of old friends/acquaintances that you lost touch with and suggest to reach out to them.
I think the latter is at least as important as keeping vital communication with those closest to you at the moment. An app could keep the balance by presenting you a rotating "mix" of your currently active and once lost, passive contacts to reach out to on different days and also those in between the two categories.
Unexpectedly seeing a picture of an old friend on your phone's screen would cheer you up. I'm just not sure how the app would get proper pictures to display, it could either enlarge those existing as profile pictures in chat apps or download some from social media sites, but the latter might cause some privacy/copyright issues if the app was doing this automatically. However, the ability of such an app to silently manage pictures of your contacts in the background is necessary to keep the surprise element.