Ideally, these questions would be written as "I want to do X. My constraints and goals are Y and Z. What should I do?" The questioner should avoid making assumptions about the best way to solve the problem, and focus on describing the goals, requirements, and constraints. In other words, the questioner should avoid making assumptions about what form the solution will take, and the questioner should be specific enough to provide all relevant information. Deviating from these guidelines tends to lead to lower-quality questions. For example, if the questioner assumes that the solution will take a particular form, he might be tempted to ask a question whether there exists any scheme of that particular form; those kinds of existence questions should be discouraged.
On the other hand, if the question is "Does there exist a cryptographic scheme that meets security notion X?", that kind of question might be on-topic if it seems likely to be of interest to our community. The answer might be yes (with an example of such a scheme), or it might be no (with a proof that it cannot be done).
Unfortunately, it looks like the sort of questions we're getting so far don't really look like the sort of questions we'd want to encourage more of. The questions we've gotten so far might not be a perfect fit for this site -- but nonetheless, I would be hesitant to draw a strict rule against all existence questions.