“Quick Adds” must above all be quick so I think this is the right question to be asking. Although being able to optionally change where the new item goes is still valuable, I should be able to hit the hotkey, press return, and keep moving.
My ideal would be both #1 and #3. There has to be a default Inbox Document for users who haven’t set anything up, but those who want to integrate that Inbox with their other documents more closely can designate one of their own as the Inbox. However I realize that’s “asking for the moon” and if we just started off with #1 alone that would still be a big improvement.
A different way of doing it perhaps: We already have a “default” Board for mobile. Having another “default” entity – but this time a Document – could start to feel a little scattered or overwhelming. What if the “default” inbox was actually a Board? Boards must always be pointed somewhere, and that can start off being a default “Inbox” document – but user can re-point the Board at any time using the existing UI.