Most of these ideas may have already occurred, but here it goes:
duplicate the builder page
have a trash for the deleted pages unintentionally
have a content block where we can by a free field of design (with wysiwyg)
have a content block directed to insert buttons of social networks, already with some examples (type add this)
Another thing, I had to adapt the JA BUILDER in the JA MONO template, and when installing the builder I altered the margins and padding of the general page. (I think it should be limited to the contents of the builder only)
For now this is it, if I remember more I edit this message.
Not sure if I got your last message correctly but JA Builder already provides Import/Export feature so that you can duplicate a page by exporting an existing page and import to a destination page as you desire.