I feel that unregistered users should have the ability to delete their own posts subject to the usual rules of registered users namely a question not having an upvoted / multiple answers. I can't think of too many avenues of abuse but maybe to stop "delete as soon as my homework is answered" it could be limited to questions without any answer. The situations I often see that this would solve are:
An unregistered user posts an answer that should have been a new question, someone points it out in a comment and they go ahead and post as a question but they can't delete the "answer". It often causes additional confusion because many users mention they can just delete it without realizing they can't.
Someone asks a question and minutes later there's an edit "never mind I worked it out" and they're normally the sort of trivial questions without any lasting value, but even if there was the community could vote to undelete the same as a registered user.
I did find a near duplicate to this question called New/unregistered users should be able to delete their own answers but it was tagged bug so marked status-by-design by Jeff close to six years ago. Considering the bug tag the main part of Jeff's response was:
Cookie-based accounts don't support voting, therefore they don't support deletion.
So if you want to nag the user to register so he or she can delete their own stuff, feel free to do so.
But he didn't give any underlying technical reason it's not possible, and if that also means that an unregistered user can't give a binding close on a duplicate vote I'd support changing that too. It seems to be a waste of both diamond and community moderators time to have to clean up posts from an unregistered user when they could resolve it themselves the same as a registered user.
