I like it how it is because filters and sensible organising of inboxes is not hard.
Not interested in email streams at all. I'd prefer to keep streams for the kind of information that doesn't require action or response frequently per item. Emails often require action or attention, and it's far better they exist as subject line items in a date-ordered list for easy retrieval, sorting and archiving all at once.
It's just a bit of message passing, why should email NOT also handle multiple participants and almost-real-time conversations well?
Twitter is a different beast, it's a public stream, but what does FB messenger offer over email, other than an improved user experience? (for some value of improved...)