If I have a Task due Today, and accidentally move her under a Parent task, then remove her from the Parent task - the original Task loses her due date and disappears to the Inbox.

This ought not occur, because nowhere in those steps above did I declare the Task was no longer due Today - I merely said the Task was (or was not) associated with the Parent task.

(FYI - the Undo option did not appear after Parent was assigned)

I propose cessation of this automatic removal of due date ... and now I'm pondering whether subtasks are allowed to have their own due dates in Bullet...