Before we can posit any solutions to the problems that I have noted in these posts, we need to at least know what questions we are trying to answer. To me, the main question is:
What should happen between the search box and the bibliographic display?
If you took a course in reference work at library school (and perhaps such a thing is no longer taught - I don't know), then you learned a technique called "the reference interview." The Wikipedia article on this is not bad, and defines the concept as an interaction at the reference desk "in which the librarian responds to the user's initial explanation of his or her information need by first attempting to clarify that need and then by directing the user to appropriate information resources." The assumption of the reference interview is that the user arrives at the library with either an ill-formed query, or one that is not easily translated to the library's sources. Bill Katz's textbook "Introduction to Reference Work" makes the point bluntly:
"Be skeptical of the of information the patron presents" 
If we're so skeptical that the user could approach the library with the correct search in mind/hand, then why then do we think that giving the user a search box in which to put that poorly thought out or badly formulated search is a solution? This is another mind-boggler to me.
So back to our question, what SHOULD happen between the search box and the bibliographic display? This is not an easy question, and it will not have a simple answer. Part of the difficulty of the answer is that there will not be one single right answer. Another difficulty is that we won't know a right answer until we try it, give it some time, open it up for tweaking, and carefully observe. That's the kind of thing that Google does when they make changes in their interface, but we haven't got either Google's money nor its network (we depend on vendor systems, which define what we can and cannot do with our catalog).
Since I don't have answers (I don't even have all of the questions) I'll pose some questions, but I really want input from any of you who have ideas on this, since your ideas are likely to be better informed than mine. What do we want to know about this problem and its possible solutions?
(Some of) Karen's Questions
Why have we stopped evolving subject access?Is it that keyword access is simply easier for users to understand? Did the technology deceive us into thinking that a "syndetic apparatus" is unnecessary? Why have the cataloging rules and bibliographic description been given so much more of our profession's time and development resources than subject access has? 
Is it too late to introduce knowledge organization to today's users?The user of today is very different to the user of pre-computer times. Some of our users have never used a catalog with an obvious knowledge organization structure that they must/can navigate. Would they find such a structure intrusive? Or would they suddenly discover what they had been missing all along? 
Can we successfully use the subject access that we already have in library records?Some of the comments in the articles organized by Cochrane in my previous post were about problems in the Library of Congress Subject Headings (LCSH), in particular that the relationships between headings were incomplete and perhaps poorly designed. Since LCSH is what we have as headings, could we make them better? Another criticism was the sparsity of "see" references, once dictated by the difficulty of updating LCSH. Can this be ameliorated? Crowdsourced? Localized?
We still do not have machine-readable versions of the Library of Congress Classification (LCC), and the machine-readable Dewey Decimal Classification (DDC) has been taken off-line (and may be subject to licensing). Could we make use of LCC/DDC for knowledge navigation if they were available as machine-readable files?
Given that both LCSH and LCC/DDC have elements of post-composition and are primarily instructions for subject catalogers, could they be modified for end-user searching, or do we need to develop a different instrument altogether?
How can we measure success?Without Google's user laboratory apparatus, the answer to this may be: we can't. At least, we cannot expect to have a definitive measure. How terrible would it be to continue to do as we do today and provide what we can, and presume that it is better than nothing? Would we really see, for example, a rise in use of library catalogs that would confirm that we have done "the right thing?"
Notes*Modern Subject Access in the Online Age: Lesson 3
Author(s): Pauline A. Cochrane, Marcia J. Bates, Margaret Beckman, Hans H. Wellisch, Sanford Berman, Toni Petersen, Stephen E. Wiberley and Jr.
Source: American Libraries, Vol. 15, No. 4 (Apr., 1984), pp. 250-252, 254-255
Stable URL: http://www.jstor.org/stable/25626708
 Katz, Bill. Introduction to Reference Work: Reference Services and Reference Processes. New York: McGraw-Hill, 1992. p. 82 http://www.worldcat.org/oclc/928951754. Cited in: Brown, Stephanie Willen. The Reference Interview: Theories and Practice. Library Philosophy and Practice 2008. ISSN 1522-0222
 One answer, although it doesn't explain everything, is economic: the cataloging rules are published by the professional association and are a revenue stream for it. That provides an incentive to create new editions of rules. There is no economic gain in making updates to the LCSH. As for the classifications, the big problem there is that they are permanently glued onto the physical volumes making retroactive changes prohibitive. Even changes to descriptive cataloging must be moderated so as to minimize disruption to existing catalogs, which we saw happen during the development of RDA, but with some adjustments the new and the old have been made to coexist in our catalogs.
 Note that there are a few places online, in particular Wikipedia, where there is a mild semblance of organized knowledge and with which users are generally familiar. It's not the same as the structure that we have in subject headings and classification, but users are prompted to select pre-formed headings, with a keyword search being secondary.
 Simon Spero did a now famous (infamous?) analysis of LCSH's structure that started with Biology and ended with Doorbells.