Most of humanity has constantly been forgetting most of the conversation they've had with their loved ones. Maybe it is not reasonable to try to hold on to the literal incarnation of daily banalities.
It's like an extension of everyone photographing every single moment of their life just because they can. Are you really going to look back over the chat log for naming your dog?
Chat history is useful for me if I was talking to a friend about a technical problem and want to review the conclusion or possible link. I've never personally delved into chat history for any other reason (perhaps a funny photo link). I've had some hilariously fun conversations on chat, but never felt the desire to relive them. I guess I'm saying if you don't actually revisit your chat history, there's really no need to feel so attached.
On a more serious note, I also think chat logs and email are important, but I can't understand why people trust all that stuff to a third party? (I do understand why people give up any idea of privacy by giving a third party access to it, I just don't understand why the let that party have what amounts to all the copies and/or use as system that while it can be backed up, can't be replicated (If you copy your gmail via imap, you still loose something wrt. organization -- you won't be (easily) able to resume your workflow without gmail -- in contrast if you use free software you will at least have the option of hosting everything yourself in an equivalent manner).