1:1's are only effective if they are private. Without the privacy, the honest conversations that move the business forward cannot happen. This is why when we introduced sharing, we included a way to keep the conversation from the public record.
An off the record conversation stays just between you and the other member of your 1:1; the two of your are the only ones who can view that part of the conversation.
A shared conversation can also be taken off the record post share. It will be like the conversation never existed. The public and team will no longer be able to see it and it will be removed from any feeds.