If we're implementing this feature, why don't we also require that users have at least 1.5 times the amount of reputation needed to ask their current question in order to answer their current question?
I believe this would really reduce the amount of non-answers that should have been edits to the original question, or perhaps a comment under another answer.
Inspired by marcog's excellent suggestion under Jeff's answer, perhaps it would make more sense to set a minimum amount of time that must pass before you can answer your own question. New users would need to wait in the neighborhood of six hours, while users with more reputation could answer their own question within minutes if they discovered the solution on their own.
This would get in the way of the behavior that we don't want, which is people posting answers that should have been edits while not annoying most.