Why is there a reputation requirement to delete your own question, particularly if it has no answers? It seems like something even unregistered users should have the right to do unilaterally, and I don't see any potential for abuse. But maybe I'm overlooking something.
There is no reputation requirement to delete own post. There is a technical obstruction in that deletion, even of one's own post, means casting a delete vote. And unregistered users cannot vote in any way, by design.
I quote Jeff Atwood:
If you want to delete posts (remember, a delete is considered a vote) then you have to use a registered account.
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.
I know this ends up being one more "support task" for active members: explaining to unregistered users that instead of blanking out their question or replacing it with garbage they should click on that link on top of the screen nagging them to register... This is one of reasons I proposed to require registration to ask a question.
It has been abused before.
Somebody posts a question that comes from homework or an exam. Somebody else takes a lot of time to write a great answer to the question; the OP reads and copies the answer, then deletes the question to cover their tracks.
Deleting questions with no answers is less problematic but can still lead to annoying situations, e.g. a question gets asked that receives a lot of down and close votes, so the OP deletes the question and asks it again unchanged.