I understand the reasons why you cannot delete a question that has answers as the people who posted the answers did so in good faith, but how about being able to disconnect your user account from the question or make the person who asked the question anonymous?
Let's say (as an example) I asked a question on car maintenance that I no longer want to come up when someone does a search on my profile as I am looking for a new job and actively posting on stack overflow so they may think that what I posted on the other site was dumb/stupid/offensive/some other reason?
It would be good if you could make you you user account 'Anon' with a stock icon for just that question. Obviously you will no longer receive notifications about this question but so what? As long as you have accepted an answer it doesn't really matter.