Unaffiliated (as it were) job applications?

Given concerns raised about the influence of "pedigree" on one's future job prospects, the role of class in shaping interviewers' expectations, and so on, here's an idea: should we strip such information from job applications during the initial phase of the search? Completely? 

How this might work:

1) On the candidate's end: no institutional letterhead; no mention of institutions on the CV or in the letter.

2) Letters of recommendation: Entirely anonymous.  Letters are signed on an entirely separate sheet, not forwarded to the search committee; no institutional letterhead, no mention of institutions.  

3) At Human Resources: for record-keeping purposes, candidates may register their institutional affiliations in a separate document/online form that would not be viewable by search committees; similarly, a candidate's referees' names/institutions would be available to HR, but not the committee.  

It's not really possible to make the candidates anonymous, as it would take all of five seconds to Google their publications or conference presentations.

Pros:

1) Would reduce, if not entirely eliminate, unjustified bias towards particular graduate (and perhaps even undergraduate) institutions.   

2) Would divert attention from the signature on the letter of reference to the letter itself.

3) Would level the playing field a bit for academics who, for whatever reason, found themselves restricted in their choice of graduate school by geography, family obligations, etc.

Cons:

1) More files for HR to maintain (or lose...).

2) Some universities not in the overall top twenty may well have individual departments with high rankings (an obvious case is Illinois State University at Normal, which has one of the most important programs in children's literature in the country).   Students in those programs would lose an advantage.

3) In some cases, stripping affiliations might make it harder to diversify programs (for any sense of the word "diversify") than easier--while search committees might have fewer opportunities to be (un)consciously biased, they would also have fewer opportunities to conscientiously identify students who are not from the top ten (if that is understood to be a goal).

Other thoughts:

1) Depending on HR regulations, it may be necessary to contact referees at some point in the decision-making phase.  Presumably, HR could identify the referees at that point.

2) I don't think this makes forgery/other forms of misrepresentation easier.  

3) There may be unforeseen consequences for applicants who share referees, in the sense that it would become difficult to catch when a referee insists that all his students are the awesomest awesomes who ever awesomed, or whatever.  By the same token, it also makes it harder for a committee to figure out that Professor X just writes terrible letters, as opposed to writing a terrible letter for one student and amazing letters for all the others.  

4) I do wonder if this approach would have unforeseen consequences in regards to professionalization trends.  On the one hand, all those ABDs from Yale with no publications would lose any advantage they might have from the magic word "Yale"; on the other hand, graduate students might feel even more pressure to publish than they do, as that would probably take the place of University Name Here as a convenient sorting hat.