From Should Questions And Answers Show The Author?
From the SO FAQ
Reputation is a (very) rough measurement of how much the Stack Overflow community trusts you. Reputation is never given, it is earned by convincing other Stack Overflow users that you know what you're talking about.
Jeff says it pretty clearly. Rep and owners are CRITICAL PILLARS of the SO formula.
From Optional anonymity to hide ignorance
I feel like 'Anonymous posting area' would end up becoming a bathroom wall of posts. Anyone who is frustrated or angered by something could seek refuge there.
Celebrity
Let's start with an easy question:
Is Reputation A Valid Measure Of Skill? NO
Reputation is an amalgam of many things, only one of which is skill. The true measure of skill resides in my posts. I take pride in all my posts. If any prospective employer were to ask about SO, I would be able to ask them to pick a random post of mine and judge me based on that.
If it becomes anonymous, I have immediately lost all that incentive. I gain nothing from posting except reputation. But, reputation means nothing unless you can point to the posts it came from.
How can you tell the difference between a user who answers two poll questions and ends up with 400 rep, versus a user who consistently answer low interest tags?
The only way to tell is by looking at their profiles and seeing what they have done. In that sense, reputation is a cover page, the user history is the actual content. Jon Skeet has certainly gained upvotes entirely from his celebrity, but if you look through his many many posts, you will discover that they are consistently incredible. This is something which he can be proud of.
We each create a persona for StackOverflow, meaningfully or not, it is the person we want to be perceived as. The only reason jjnguy was able to call me out in his answer was because my posts have my name on them. The only reason I was able to identify that it was a friend calling me out was because he has his name on his responses.
Hiding in Anonymity
How many posts have you seen where you feel like saying "I would suggest that you Peruse The User Guide". I would never do that, first of all it's rude, second of all, it's me saying it. But if anonymity was created, then there is no disincentive for me to be hideously uncouth. I could even create sock-puppet answers.
"Person A": This is ridiculous. Your mother was a hamster!
"Person B": Unlike (Person A)(Link) I believe this question is valid. There are blah blah blah, blah blah!
This makes "Person B" seem wise and measured. When really it's the same person. Even if we forbid multiple answers on one question, the disincentives are reduced.
As noted before, if I cannot brag about the quality of my answers, then I don't have a real incentive to create quality in my answers.
Verification
Most question are easily testable (they are supposed to be) but this is not always the case. It occurs in some cases that the implications of testing, POCing, sandboxing, or implementing a solution could be costly and expensive. In this case, I want to know a little about the people who are answering. Obviously I don't know everything about them, but if I am able to see that one user has gained his reputation in single upvotes over thousands of spam-like answers, and the other user has gained her reputation in a remarkably short time with inpeccable answers, then I would be inclined towards her answer. Is this a reason for me to consider both answers? No. But it does give me a little meta information about who is answering the question.
With anonymity, I lose that history.
It is important to note that I'm not advocating blind faith based on past performance. I'm simply saying that in important cases where you need extra information, it would be nice to have it there.
Infamy
The downside. We aren't supposed to consider a user's past behaviour. In fact, I've been railing against that very concept for a week now.
Good Advice is good advice, regardless of the source. But for those of us who are working with someone else's money and time sometimes need a little bit extra. Again, this is not to say it is appropriate to comment, downvote, edit, disregard, or in any way modify your behaviour based on a user's past performance. This is simply regarding the actual moment of implementation.
If the user has been consistently atrocious, it may be necessary to take precautions. You should never pre-judge, however.