Right now, all of it is ending up in email anyway, except for SMS (maybe -- googlevoice can route your SMS to email). So you get the disadvantages of archiving all that crap (which actually turns out not to be that bad -- my gmail acct is only half full, and it even has wordpress database backups routed into it) without the advantages.

(Surely writing a rule to automatically throw away old voicemails, say, is pretty easy.)