This is not a duplicate of questions asking about features that would allow users to post anonymously or about whether or not anonymous posting is allowed. I am asking why should the user/reputation system exist, if the ideology behind anonymous voting is truly valued.
I get why votes are anonymous. Users should be able to cast their votes without worrying about being judged for their votes or lack of votes. Votes should only reflect the quality of the question, answer, or comment being evaluated.
One might ask why are votes displayed publicly anyway (as opposed to being only shown to the user that posted the question). Wouldn't someone go into a post that has 400 upvotes with a certain bias that might affect their genuine evaluation of whether they actually consider it to be a good post? This is different, as this induced bias is not that influential, and the genuineness of votes cast on SE would not really matter if votes themselves didn't exist. So yes, hiding votes from the public would make votes marginally more genuine, but would eliminate the importance of vote genuineness.
So why is vote genuineness important? The point of Stack Exchange is not only to exchange information between users, but is to document that information and share it with the entire internet. Vote totals can be a credibility meter for someone researching who finds a Stack Exchange post that does not draw on cited sources but on personal experience/information (as many, maybe even most SE posts do). They can trust that a good voting score on a site with generally credible communities as a whole equates to a credible answer.
One can only assume that approval by a generally credible community equates to a credible question if the votes of that community reflect only the quality of that post. That is why voting genuineness is so important on this site. If Stack Exchange were like Facebook, where people upvote other people's posts because they are friends or because they respect or admire other users (or otherwise in the negative respect), then people drawing on information from this site cannot be sure that a post's voting score reflects the actual quality of that post.
But now to my main question: if voting genuineness is so important, then why are usernames and reputation scores even displayed publicly? While there is no reason why reputation and privileges should not be recorded privately, the public display of identity and reputation can harm voting genuineness in many ways.
As a side note, I will use the term "numeric reputation" to reference your SE reputation score, and "non-numeric reputation" to reference your actual reputation among the SE community/ies. Numeric reputation is indicated by a user's rep score, while a user's non-numeric reputation is tied to their username/identity. The two are usually correlated but not the same.
It cannot be denied that someone would be more likely to downvote or vote to close a question by someone with 40 reputation than they would one by someone with 20k rep. They might assume any flaws in a higher rep poster's post was just a one-time mistake and would be less likely to insult their non-numeric reputation with a downvote/close vote. They might not want to risk their own non-numeric reputation by challenging someone with a high numeric and non-numeric reputation. On the other hand, someone might be more likely to downvote a 40 reputation user who has't made many posts, or has made numerous bad posts because they do not think they deserve the reputation boost. This would hold true even if that user's post was a good one. A similar phenomenon holds for upvoting; someone would be more likely to upvote a respected member of SE to motivate them to continue their positive contributions than they would someone who just joined or who has a bad numeric or non-numeric reputation. All these influences on voting are not dependent on the actual quality of the posts in question, decreasing vote genuineness.
The non-anonymity of user identity and reputation causes many of the problems with SE discussed in this article. That being said, changing the user/reputation system would certainly take away some of the appeal of participating on Stack Exchange, as it cannot be denied that many users value the reputation they have built in their respective communities, just as they value their raw reputation score as a number they can be proud of personally or use professionally. A quote from Jeff Attwood:
One of the major reasons we created Stack Overflow was to give every programmer a chance to be recognized by their peers. Recognized for their knowledge, their passion, and their willingness to help their fellow programmers get better at their craft.
In my view this is an important problem, and while I am not suggesting taking away the reputation system from SE, the problems with SE that are revealed when considering it are important to address.
I understand that this question may be too broad or subjective as there really is no one correct answer and it is more prompting a discussion, but given that this is meta SE and not a specific SE site and because I see this as an important issue I assume that it is an acceptable bending of the rules.
Edit: I now realize this may be a duplicate of this post (although not exactly the same). Maybe this post should be moved there?