When I initially read this post (quite a while back) I was strongly opposed to writing critiques - it seemed like something better reserved for a forum than for Stack Exchange. Maybe it is, but after reading Does a Writers Stack Exchange even make sense? and Is writers.se in risk of failure? I started thinking more about the strengths and weaknesses of the Stack Exchange learning format, which led me to reevaluate the question posted here. Here are my thoughts:
If we don't allow for something along the lines of a critique, eventually people are going to run out of questions to ask and answers to give. I own a huge number of fictional writing books at home. The vast number of them address the exact same thing: characters, viewpoints, dialogue, plot, structure, description, setting, character building, editing, and publishing advice.
Book after book covers one or more of these topics - and that's it. And honestly, the number of questions raised in these books are fairly limited - it's just bringing a different author's perspective to the same old questions. About the only "objective" books I've got (ones where the answers are almost always consistently the same) are the books on publishing advice - everything else depends on the author and his/her own style.
It seems like the rate of questions are dying down quite a bit. Many of the big questions have been asked - sometimes more than once. More specific questions are being asked, but one of the problems with asking very (good) specific questions is that you have to know something to ask them. Oftentimes, the measure of a person's knowledge is not determined in the answers they have, but rather the quality of their questions.
As an amateur writer, I don't know what kinds of questions to always even ask about my work. That's why critique circles are so important. They don't just teach me what to do better - they actually teach me what questions to ask about my writing.
I don't know that there are enough experienced writers and authors on here to ask the more specific and (possibly) important questions - I'm not even sure what those questions might be! At the same time, the better the question (in this regard), the more knowledgeable the people you need in order to answer them. I can give my input about certain fictional writing questions - but there comes a point where it's just out of my league. I imagine that's true for a lot of people on here. And, unfortunately, if some of us did try and answer those questions, you'd probably just get bad answers.
Critiques are where authors really live and learn - I don't know a lot, but that much I do know. Every good advanced college writing course focuses on critiques and addressing specific prose - either a student's, the teacher's, or another author's.
I feel like a broken record saying this, but: I don't really know exactly how to fix this problem, either - those are just my thoughts on the matter. I'm not sure broad, open critiques are the way to go. It seems like SE isn't built well for that. On the other hand, banning critiques binds especially us newbie, amateur writers in that we probably aren't going to know what specific kind of questions to ask most of the time without help and guidance.
It seems like there ought to be some sort of middle-ground.