If you meet a new person and want to exchange messages, there's not a huge difference between adding them in your messaging app and adding them to your contact list.

Using this model it would better to have multiple lists though, or at least tagging within the general contacts list, so tag-based lists could be allowed by certain apps (to keep business and personal messaging separate for example).

Facebook messengers chat requests has basically solved this problem.

New person goes to chat requests, they communicate through another channel they've sent you a message, you go open the graveyard of chat requests and accept theirs.