(Much of this answer comes from a discussion in chat with Rubio, Brandon_J, and North.)
I see several problems with the "open-ended" format. But first, a definition, to make sure we're all on the same page:
An open-ended question is one where multiple answers are expected; answers are ranked by some sort of rule, and the answer with the best score by that ranking is the accepted answer.
(Without the second part of that sentence, it's just a question that is intentionally too broad. These are already disallowed.)
So, what problems do I see? Well:
Dependence on other answers
In open-ended questions, an answer can be invalidated by other answers. If Answer A scores 18 points on whatever scale a puzzle used, and then answer B is posted (scoring 19 points), then Answer A is retroactively no longer a correct answer.
Compare this to regular puzzles: if someone posts a strategy for a "prisoners and hats" puzzle, it does not get disproven because someone found a simpler strategy. An answer there can only be invalidated by an inherent problem with that answer, not just "not being as good as this other answer".
Similarly, for another comparison, if someone posts a partial answer (to, say, a crossword), and then someone else posts a full answer, the partial answer does not become wrong. Even if the partial answer was posted after the full answer, the partial answer is still correct.
One goal of Puzzling Stack Exchange is to be an archive of high-quality puzzles that are solvable at any point in time, whether it's immediately after the puzzle is posted or ten years later. This seems to me to be in direct conflict with that: an answer at the start is not necessarily an answer later. Which leads me directly to another reason:
How do you know the best answer is the best?
With these questions, you can almost never know when an answer is correct. It's always possible someone can come along a year later and one-up an already-posted solution. So these questions are implicitly of the form "What's the best way to do X... that the PSE community has thought of so far?". That's why the ranking system exists: it allows you to pick out of the answers of the PSE community, not
So the top answer is in the same position as all of the other answers were: it's always waiting to be outdone. open-ended questions don't have a clear correct answer, and having a clear correct answer is a quality necessary to be a puzzle. And speaking of which...
These aren't puzzles. They're games.
open-ended questions may be fun things to think about. But they're not puzzles. As Rubio put it:
The danger - and I think we're correct to avoid it, and it's something Deus alluded to in an earlier comment - is that instead of a puzzle what we really have is a game: find the best thing you can come up with. (I've even seen some that are: best solution in days is the winner)
There is no "solution" to these questions, and that's by design. They're meant to be fun things to think about, but they're fundamentally not a thing that can be solved. Unless you have a proof of optimality (which the question is generally not designed for), all you can do is incrementally improve on previous answers and hope that nobody will improve on yours.
We don't treat analogous situations the same way.
I've already pointed out that we don't allow other questions without a single best answer. (Note that the ranking system doesn't satisfy this: it allows you to find a single best answer out of the ones posted by PSE members, but not a best answer in general.) We don't allow other questions whose answers change based on the answers that PSE members have posted -- that wouldn't be a self-contained puzzle. It's why semi-interactive-puzzle was deprecated.
Consider a question that starts like this:
Here are 20 lines taken from various riddles. What object fits the most of these lines?
Assume, for the sake of argument, that whether something fits a line is generally not up for debate: they're fairly clear qualities like "this object is smaller than a breadbox" or "this object is green".
This question should probably be closed. Yet this seems completely analogous to, or even better than, open-ended questions as we have them. Any problems this question has apply equally to open-ended questions, yet we allow the latter.
The inevitable problem of HNQ
open-ended questions attract many answers. This is one of the criteria used to pick questions for the Hot Network Questions list, which is the first impression many Stack Exchange users get of Puzzling. We're putting our worst foot forward here, and showing questions that are (hopefully) not representative of the rest of the site's content.
There's unfortunately no way to show that this is driving people away without something to compare to. But I know that if my first impressions of the site were open-ended questions, I probably wouldn't have stayed.
So why do we make this exception? Why do we allow the tag open-ended to absolve askers of all responsibility for making sure their questions have solutions, and let them break some of the core principles of PSE (solvability at any point in time, a single best answer, self-contained puzzles)? I don't believe that there's any benefit to keeping these.
In the aforementioned discussion, we eventually came to a conclusion that would draw a fairly clear line, while still allowing well-designed optimization questions. There are three things that might be called "open-ended" questions, that we'd still like to allow:
These should have a provably best answer (ideally, not one that needs heavy programming or mathematics to prove, in the same way that we currently don't want puzzles that require heavy programming or mathematics to solve). Answers should come with justification of why they are optimal; an answer without this is not a full answer, but more of a comment.
- Questions about whether something is provably optimizable
These are allowed, but answers are of the form "yes" or "no", with justification. Again, "you can get this much but I'm not sure if you can do better" is a comment, not an answer.
- Questions about puzzle design that might have many possible answers
Here, we can follow the same rules as other sites on the SE network. These questions should not be asking for solutions to puzzles, but for the best way to accomplish some sort of design for a puzzle.