I'm Grace Note, a Stack Exchange Community Manager.
In a usual case, we allow users to delete their own posts at any point because, well, it is their post. In the case of questions, we prohibit such deletions when there are upvoted answers for twofold reason. One, because doing so usually destroys valuable information that people spent time producing. Two, unrelated to here, but anyway, getting a great answer and then deleting it so that one keeps it for one's self is rude and antithetical to the mission of the site. Granted, this is kind of a derivative of the first reason but it speaks directly to why this prohibition overrides "I should be allowed to delete things because they're mine".
Moderators can go around these restrictions to delete things which, well, need to be deleted. For any number of reasons. Point is that they are the voice of the community and act as exception handlers, which is precisely what it is when a question gets a good answer but should be deleted† - an exception.
†Ohohohohoho! You were expecting a footnote! Too bad, this is happening right here! When does a question reach a state where it should be deleted? There's the obvious off-topic entries - a great answer doesn't make a question on-topic at the end of the day, we aren't going to host the world's greatest rabbit stew recipe because someone happened to provide it to an off-topic question. Outside of this kind of case, it then becomes whether or not the answer is great enough that it warrants keeping a junk question. For example, the question that brought this about, the answer is essentially a glorified "no", which while truthfully the solution, is not a whole much that deserved grand praise to save what even the question author believes is a question that wasn't worth asking.
There are two vehicles to which this can be addressed then - flags and Meta. A flag for moderator attention gets it directly to the moderators and would be great when "This really should be deleted but I cannot!" is pretty clear cut. Meta would bring the situation to a larger community review, which would allow for discussing the merits of keeping the question around versus deleting it on shakier grounds. It's not always a straight answer and community discussion is the primary method of hashing out what the community figures for this kind of thing. These are what avenues one should look at when they wish to delete that which they may not delete.
In a general case, we usually do not want to delete questions that haven't actually gotten closed - as we actually have the whole delete voting process for this primary situation that entirely defines what closure is. Non-closed deletions are generally for either obvious trash that must be disposed immediately (the 20k privilege's design intent), or self-deletions. Since obvious kills aren't anything that usually warrants discussion, this sort of "Let's agree to be rid of this" should really only come up as a result of a question author failing to be able to remove a question that said author wishes to remove.
Dissociating a post is a thing that can happen, as mentioned in comments. In most cases deletion is sufficient, but if necessary it is possible for a post's ownership to be dissociated manually, resulting in an empty authorship to the post and freeing up the reputation change from votes to the original author. I would recommend this is not generally looked at except for extenuating circumstances, as by nature of the process it results in the destruction of portions of history and tracking of posts and users. As stated in this very paragraph, in most cases deletion should be sufficient.