Intent behind Recommendation Letter requirement?
At a minimum, a letter of recommendation is no worse than, say, a Yelp review.  The person who rated Joe's Hamburger Shack 5 stars is a total stranger to you, but knowing that that person liked it is still more data than you previously had about how good the place is.

For a grad school application, there are few sources of concrete information.  Hard data like grades, GPA, and GRE scores cover only a fraction of the relevant qualities of each applicant.  It can certainly help if the admissions committee knows the recommender, but even if they don't, the mere fact that that the applicant is considered qualified by an active researcher at an accredited instituion is a significant gain over the other information available in the application.

Also, as Nate Eldredge mentioned in a comment, a good letter will not just state the belief that the applicant is qualified, but will give reasons.  These reasons, again, come from a person who is presumed qualified to evaluate them, and are therefore more valuable.

It is true that if not only the recommender but also their institution is totally unknown to the committee (e.g., a recommendation from Prof. John Doe at East Podunk Community College), the information may not be helpful, and could even be viewed skeptically.  But I don't think this is a common case.  Even if no one on the faculty personally knows or has collaborated with any professors at, say, Harvard, you can bet that it means something to have a Harvard professor recommend someone.  Although that's an extreme case, the same principle applies to other schools in varying degrees: even knowing that the school exists goes some way towards establishing credibility.

How much weight these are or should be given is debatable, but there is simply no other way to get the information in recommendation letters, namely a qualified professional's judgment of the applicant's quality.  It may indeed be that in some cases the committee views the letters as unhelpful because they are too vague, but if many letters are informative, then vague letters are already "bad" in comparison, and provide a means of winnowing the applicant pool.  Even in a hypothetical case in which only a few letters were helpful, the school doesn't really stand to lose anything by having them, and stands to gain useful insight that they can't get any other way.

Also, I would be interested to see some numbers on how often the admissions committee really does not know and has never heard of any of the people writing the letters.  An important thing to consider is that in many cases one or more of the letter writers will have been consulted by the applicant to get advice on where to apply.  Thus, there can be a self-selection process at work: professors know professors at other institutions, thus they advise their students to apply there, and then they write a letter of recommendation.  I would guess that this significantly increases the likelihood that some of the letter writers will be known to the admissions committee.  In effect, the same people are not only recommending the applicant to the school, but recommending the school to the applicant (by suggesting that they apply there).

A little edit: Based on your comments, it seems you are also worried about situations where, e.g., the letter writer is "biased" towards recommending the applicant.  There are two responses to this: one is that everyone knows that.  The recommender wouldn't be writing the letter if he were biased against the applicant.  The recommendation is not supposed to be "impartial" in the sense that it mechnically assesses some attributes of the applicant.  It's just supposed to be the honest opinion of a real person who interacted with the applicant in a real academic context.

More generally, there is simply no getting around the fact that virtually everything in academia operates on trust.  When you submit an article to a journal, the editor has no way of knowing whether you plagiarized the text, falsified the data, etc.  When you apply for a job and list dozens of publications on your CV, the search committee probably does not look up every single one ot make sure it really exists.  For better or for worse, academic procedures are built on the notion of receiving "credentials" that indicate you are to be trusted.  When someone receives a letter signed "Prof. John Doe, XYZ University", they assume that Prof. John Doe really is a professor at XYZ University.  It is of course possible to fabricate such credentials, but to handle that problem would require a complete overhaul of academia.  The basic reason people trust a letter-writer is because academics trust each other not to tell brazen lies about who they are, where they work, etc.  They understand that the recommender may not be totally objective in his or her assessment of the candidate, but they nonetheless assume that the assessment is made in good faith by a qualified judge; that's all that matters.