FINAL EDIT
Thanks for the great answers explaining the concept behind SE and its goals.
However, when it comes to the negative feedback (specifically the downvoting) I think - even in light of the explanations - it's still unhelpful.
The same curation goals can (absolutely IMHO) be accomplished with upvoting alone. But it is the encouraged negative feedback that creates the general mindset of negativity you're attempting to combat.
Put in another way; one can't say it's OK to throw stones, and then be frustrated when the general populace can't (or refuses to) differentiate between the stones you want thrown, and the stones you don't.
===Original post===
TL;DR Can a website which has been founded in the idea of supporting negative feedback as strongly as positive feedback - actually solve the now-very-negative attitude of the site with a CoC?
===
I've been a Stack user for many years as an IT and development professional, and have accrued a moderate reputation. I've also been a technical team leader and nerd herder for more than a decade.
While I applaud Stack's attempt to make the site more inviting, I wonder if a new CoC is not just bandaids and pretty wrapping over a deeper issue.
When Stack Overflow was founded in 2008, there hadn't been much research into how to manage the huge volume of information that passes through forum-style sites. The idea of a community-corrected site, using volunteer moderators - and where both both positive and negative feedback was employed - was highly successful.
However, the encouragement of the "negative feedback" mindset is - inarguably - what has led to the general feeling "unfriendliness" as seen by the internet as a whole. I was told directly by a moderator (during a Meta discussion) [paraphrased from here, see context in footnote*] that Stack's user base should be viewed as children who need to be punished for their stupidity (in order to improve their questions). This mindset is not unique in Stack.
I understand the need for a method to bring solid posts to the top, and drive poor posts to the bottom, however research suggests that positive feedback alone is more than sufficient to cause the same effect.
Quora and Expert's Exchange (before it went commercial) are prime examples of sites where quality posts cleanly rise to the top, and avoid glut and redundancy, without using a negative feedback model.
=== In conclusion... The bottom line is; many highly qualified and experienced members of my teams in the past loved Stack for when Googling a problem, but loathed asking questions - due to the inevitable hassling received for pointless and pedantic reasons. This is good for no one.
So, when the "unfriendliness problem" of the site seems to lie closer to its core mindset - will a sticker on the top saying "Be nice" really help?
- It was suggested this paraphrase was out of context. It is important to state that this is a paraphrase of the moderators opinion and not an exact quote. However, from the lengthy conversation that moderator and I had - I veleive firmly this is full this opinion of the user base.
EDIT === At the suggestion of the moderator, I'm going to add examples here. I hed initially left these out for the sake of brevity.
Down votes
While I understand the reason they were initially implemented - the web (and forum sites) are now well matured and researched. While "downvoting" may offer a small benefit for moving posts to the top and bottom of a feed - it has been shown by many, many sites that it is not really necessary to accomplish this task.
However it is inarguable that downvoting adds to the "punitive", "hen pecking" mindset of the site. There is - for lack of a better way to say it - a mindset amongst many people to criticize at all costs.
So, the question for the site owners and developer is: does the small benefit offered by "downvoting" towards one of their cited goals (curation of the site) outweigh the large destructiveness towards their other goal (site friendliness).
"Getting downvoted" is an especially large complaint, especially by noobs whose reputation my just be starting out.
Over-policing by moderators
The site MUST be policed to maintain quality. However, in recent years, many moderators seem to have devolved to the mindset that policing the site is their primary duty (versus answering questions or assisting users in becoming better users).
While following the guidelines is important, I find many, many questions that are downvoted or halted altogether for reasons of "policy violation that neither reduce the question's quality - nor would have made it better.
In fact, I can think of a dozen questions by team members in the past that following the question policies to the letter (or following the moderators suggestions) would have made the question harder to understand not better.
All regulations must strike a balance between following the "letter" of the law, and the "purpose" of the law. The site seems to have drifted strongly towards the letter, versus the goals.
Redundancy
This one is a difficult one. While I completely agree with the need to reduce a million questions asking the same thing, I have also experienced the site. And it is commonplace that one question in a subject is neither entirely correct, nor does it entirely cover the necessary problem.
In fact, nearly without exception, when I Google Stack only for answers - I find I have to read 2 or 3 very similar answers in order to find the complete solution that fixes my problem.
IN the "early days" when storage was expensive, databases overwhelmed, and Google algorithms imprecise - I would agree more with the redundancy issue.
However with the modern cheap storage, pinpoint searches, and powerful databases - killing a question outright for similarities to others seem unnecessary. Again, I can quote a half dozen questions asked by my team which were flagged as redundant (and closed down) when, in fat, they were completely dissimilar to the question referenced in the "already answered" link. Which relates to the final idea...
No method of review
I understand the moderators are volunteers, and individuals (with good and bad days), and whose time is valuable.
However, many moderators have developed a sense of inflexibility in their kingdoms. And, once a decision is made, there is ZERO recourse. I can understand this also helps avoid arguments. But in cases where the mod is, unfortunately, wrong - This leads to terrible frustrations amongst users, especially when the moderators follow them.
I myself once wrote a question, and had it closed down as redundant. However, the linked answer didn't address the problem. The automated message on the shutdown response itself suggested [paraphrased], "Try asking the question again, explaining how the answer to which it is redundant does not suffice".
I did, and it was immediately (within seconds) shut down by the same moderator saying [NOT paraphrased], "This is not how you make friends on this site."
While, again, I understand people, and bad days - this mindset of "fiefdom" has begun to be more prevalent in Stack. Which directly affects the operator's stated desire to make the site friendlier.
EDIT
@S.L. Barth "What might work better, is if you had references to actual scientific research that shows how less/no downvoting can still keep the poor content out."
Very valid point. While much of my information on this is a few years old (when I was running a web development team), Here is one link that helps support the idea. As all researchers know, "One paper does not a fact make" - but I will continue adding more as I find them again :)
Some more links, both pro and con
The Effects of Feedback and Habit on Content Posting in an Online Community