There is a market in terms of "If someone was to create a website where this was the goal and allowed, it would likely find people willing to visit it."
Before you go off designing such a website (the Stack Exchange format doesn't go well for such a type of question - by design I believe, and a good choice), I believe the naive implementation it is doomed to failure.
Read A Group Is Its Own Worst Enemy by Clay Shirky. Though a decade old, it has important truths about social software.
From this article:
And, finally, you have to find a way to spare the group from scale.
Scale alone kills conversations, because conversations require dense
two-way conversations. In conversational contexts, Metcalfe's law is a
drag. The fact that the amount of two-way connections you have to
support goes up with the square of the users means that the density of
conversation falls off very fast as the system scales even a little
bit. You have to have some way to let users hang onto the less is more
pattern, in order to keep associated with one another.
Stack Exchange works reasonably because it makes conversations difficult. You have questions and answers which is not a two way conversation - it is a question and an answer and it's done.
When the code detects a conversation happening in comments, it suggests people take the comments to a chat room (where conversations of a small group work).
From earlier in the article:
The downside of going for size and scale above all else is that the
dense, interconnected pattern that drives group conversation and
collaboration isn't supportable at any large scale. Less is different
-- small groups of people can engage in kinds of interaction that large groups can't. And so we blew past that interesting scale of
small groups. Larger than a dozen, smaller than a few hundred, where
people can actually have these conversational forms that can't be
supported when you're talking about tens of thousands or millions of
users, at least in a single group.
The question of "what language should I learn" or "what should I do next" or "what book should I read" requires a conversation to understand the context of what is being asked. The answer to "what language should I learn" is not "C" in every case. The correct answer requires that the asker and the answerer exchange a dozen messages each way.
The conversation that would need to happen is one that would be unmanageable (and thus, the reason why SE tries to prevent conversations in the Q&A part).
For an example of what this would become, head over to a forum that allows "shopping" type questions (deviant art photography forum springs to mind, though it may have changed since I was there last - Reddit may also be a place that allows this and consider what asking such a question there will result in) and look at the size and number of pages of discussion for a "simple" question.
As an aside, you may want to read Web Discussions: Flat by Design which does go into some of the difficulty with online conversations. Additionally, the M.SO post Is Stack Overflow a forum goes into the nature of what it is:
For example, on a forum you might ask how to run a game in windowed mode. You will get several responses, some of which will be nothing but "oh, I love that game!" or "I haven't played that in a while, wow." You'll be lucky if you get a relevant response. By contrast, on Stack Exchange you'd get practical responses that are 100% relevant to your question. 1
Stack Exchange neither supports nor encourages a "forum-style" of open, free-for-all discussion (many-to-many conversations). This is by design... Stack Exchange is built on the premise that forums don't scale. All those open conversations mean that those forums only tend to get noisier and noisier. What inevitably happens is... you stop learning. 2