A personal question page (as usual) and a list which remain on the users profile to build the question. Leaving the question unpublished so one can come back to work on the question, extend or, minimize or discard. When no solution is found anywhere and the problem remains the user can publish it and it will be viewable/answerable to all people.
More generalized questions as research is made easier.
rephrasing/generalizing the question after finding information
emphasizing this isn't a forum but a research (Q/A) site
User-comfort thus one can focus on his/her problem.
formatting the layout, keeps the question clear
providing already a (possible) answer
one-click-discard, actually two due to selection on this site
keeping a clear desktop
Referring to new people to use this feature
less duplicates or wrongly stated questions, due to easy research
closed due duplicates can be directly put into their own unpublished list to think delete or rephrase,
maybe down-voted too, or new decline votes
clearer insight/higher acceptance why something is 'not ready' but not disapproved, thus preventing questions like "How to delete my account, I don't like the policy", where they only misunderstanding and where they can be a valuable source in time.
new people can find easy questions much sooner, less duplicates. So related are easier found (less results).
they feel taken seriously or professional which they may be one day
warm-hearted people make better marketing
yet another server to fill
reposting of declined questions
more questions on meta
The quality of the site will rise due to fewer questions but higher quality answers, as questions are more qualified. Due to lesser questions, duplicates are notice earlier. This could have a recursive effect.
Although it might seem to be a user feature or new-user help, it is aiming at the overall quality of site.