While I'm definitely in the "encrypt and take all reasonable precautions" camp, I have to say that your example doesn't make sense to me - unless I'm misunderstanding your example, the recipient of those messages has already received a plaintext/unencrypted copy of the conversation. If the originally intended recipient is now the one holding that information "ransom", I don't know how encryption could help - at some point it was plaintext, and they could have made copies (screenshots, or even a Polaroid picture of their phone screen) at that time.

Again, could be misunderstanding your example...