The web's "curation" works (to whatever degree it does) because there are thousands, if not millions of people who can rate the quality of most articles/essays/websites. But in many scientific fields, there are often only a very small number of people who would be qualified to review a particular paper (usually well under a hundred, sometimes as few as a handful).
And make no mistake, this is a numbers game -- there's the well known 100/10/1 rule for content websites (for every 100 viewers, there are 10 who rate content, and only 1 who creates content). The exact numbers vary quite a bit from website to website, but the point is that it's orders of magnitude difference. That's all fine if your initial pool of people is huge, but if you start with 20 qualified people...you see the issue.
Another related point not addressed is that peer review is fairly demanding work. You're not just saying "accept" or "reject", but you're obliged to write a page or two suggesting the strong and weak points of the paper, things to improve, etc. You need some mechanism for enforcing this (even if it's via social norms), otherwise review quality deteriorates quite severely, which in turn affects paper quality.
In lieu of this article, I'd recommend seeing lectures by (or essays by) Michael Nielsen, who's thought about this problem in much more detail and (I believe) has a much better understanding of the way things work.