This feature used to exist, and it was removed. The intended use for community wiki questions was precisely what you seem to be suggesting: things like “what's your favorite …?”, or “let's make a list of …”. Answers were forcibly made community wiki, so they were easy to edit and the whole thread didn't confer anybody reputation.
The feature was removed because it didn't work. Even without reputation at stake, you'd pretty much always get one of two things: either the question didn't gather much interest and its answers were too incomplete to be useful; or the question gathered some interest and it had a mess of disorganized, redundant, poorly-explained answers. Voting on answers tended to reflect primarily who posted first, secondarily how superficially attractive the answer was (+100 bonus for posting a cartoon), and not much how useful the answer was.
Depending on what your not-really-a-question is, some options include:
- An ordinary question.
- A wiki outside of Stack Exchange.
- A question with a single wiki answer.
- Technically, moderators can make a question community wiki. But there would have to be a good reason to think that it would be better than the 99% that failed.