I don’t know if it could be possible for private chats, but it should for games chat.
Have you ever thought “I’d like to find that match where I played with that nice user which name I can’t recall”… or something like “I don’t remember which user told me that in the game chat”… ???
I started to send friend requests to every user I got into conversation with in game chat. The list got quite long. There are a lot of friendly people out there.