Agree! I thought this was the whole idea of the Conversations Inbox was to have a central area for your team to ensure no messages fall through the cracks. If all other chat bot conversations appear in the Inbox, why wouldn't Messenger?
I think it's a priority to integrate Social Media (at least FB MSN) and the blog's comments into the conversations inbox. It has been requested several times by some of our clients and they are moving to other solutions like Zendesk or Desk for the full performance.