Here's an experiment we could try: look at the "recent comments" feed, and do a text search on the question mark.

For instance, taking this link as starting point (because the most recent messages are biased by this very thread) we can count 67 occurrences of the question mark.

For a preliminary analysis I went through these discarding the ones in quotations, and built a list of question classes:

"challenge" questions like "how confident are you about this" - they are really intended to prompt the askee to ask the question of themselves
"clarification" questions - like "what did you mean by X"
"genuinely curious" questions - the first to seem so was "How does any particular agent go about convincing me that it's Omega?"
"mocking rhetorical" questions - like "Don't they know (...) this thing called 'social networking'? "
"hypothetical" questions - like "what would I think of an amateur who argues with me in the area of my competence?"
"question and answer" pairs - like "does that mean they are wasting their time there? Of course not..." - obviously rhetorical
"what if" questions - like "And what if you wanted to grow?"
"agreement seeking" questions - like "Agreed?"
"information-providing" questions - like "Anyone heard of Marblar?" (with a link, so we know the asker has heard of it)

Questions asked in the negative are often rhetorical (e.g. "Isn't the whole point of patents for people NOT to use them?"). Rhetorical questions are quite common but do not obviously dominate. We could push this a bit further and get some statistics.

I've considered a reversal test. Would it be feasible to signal non-curiosity instead of signaling curiosity? That is, encourage a norm that every time you were about to ask a non-curious question, you prefaced it with an explicit "I think you're a fake and I'm going to ask embarrassing questions"?

My first thought was "obviously that wouldn't work". But that's an interesting thought, why would I think that? Do I think that in fact most of the time when we ask a question it's to make the respondent look stupid?

Actually, the factual analysis suggests that "question" is a more complex category than one might first think. There are many types of question, not all of them stemming from curiosity. Combining that with the reversal test, I conclude that there might be real value in coming up with sentence forms that convey the meaning "this is intended as a genuinely curious question", and encouraging their use in the community.