I think you're really asking two questions here. You're asking if we can improve the "unanswered questions" section, and you're asking if we can deal with "hard to answer" questions in a better way.
In regards to changing the Unanswered Questions page:
Apart from the issue of "hard to answer" questions, you seem to be suggesting we order questions in order of score. From what I can see, we already do. You can select to view questions by votes, and in fact, when I view "unanswered questions" based off my tags, that list is also ordered by score.
As you have pointed out, this is irrelevant. The very same question you identify as 'hard to answer - lets omit' has a score of 17. In many of the tags it uses, this means it comes first in an ordered list.
Aside from this, I am certainly open to other ideas. That said, I do not think the unanswered questions section needs any real improvements. As it stands, I find the unanswered questions section consistent and easy to navigate. Let's not fix something that is not broken.
In regards to proposing an "archived" state:
In part, I like the idea behind it; but as has already been explained to me, such features pose further problems. I will provide reasoning, based off a few comments you have made, both in regards to the example question and the proposed feature.
- Certain issues you bring up are already covered under legitimate close reasons. For example, Stack Overflow has a specific close reason that states 'must include...code...to reproduce (the problem)'. If it is clear that important information is missing, this commonly gets flagged as too broad or unclear. If you see such issues, vote to close. If the vote does not pass, there must not have been enough users voting to agree with you. This would have the same effect in a different voting queue.
- While I always like to see an accepted answer on a question, accepted answers do not necessarily reflect best answers. Votes do. In fact, an accepted answer only gives you 5 more reputation than an up vote, and it can only happen once per answer. While it is nice to see an answer accepted, we do not necessarily need the original user to tell us which was the right answer. If we need more information, that is an entirely different ball park (see "vote to close - unclear or too broad"). It is also worth noting that questions do not appear on the "unanswered questions" page if they have an answer with a positive score.
- In theory, if we labelled a question as "archived", we are limiting the likeliness of further activity. I strongly feel some users would not bother to answer (in fact, I have previously been asked "why did you bother" for answering a question that was evidently abandoned by the Asker). We are also limiting the coverage for this question, so in turn, limiting the chances that it would receive any activity to "unarchive" it. Can you say question graveyard?
- All in all, the quality issue can be very much down to someone's opinion. For example, you state that the above question is low quality; but it has 17 up-votes, so I imagine other users do not agree.
All in all, I think it's awesome that you're going to the effort of taking these considerations, in order to help improve Stack Overflow. In regards to the suggested "archive" state, you have certainly fleshed the idea out more thoroughly than I had, previously.
My suggestion for dealing with "unanswered questions - hard to answer" is quite simple. Try to answer them. If you cannot, start a bounty, or see if linking to it from your social network might alert others to the cause.
In some cases, I have seen these questions "solved" through meta. Through further discussion, the general community is able to come to agreement on the core question; a canon version of the question (one that addresses the same question, but broad enough to apply to other situations) is posted, with an included answer, and users vote to close the original as a duplicate. This entirely depends on the site, and the range of participation in meta.