I believe questions like this may need some editing, and sometimes should be community wiki, but should definitely not be closed. It should not be impossible to ask about dialectical variations of a given term.
The issue of whether answers can be absolutely complete also seems to be missing the point to me. An answer (or a set of answers) can be complete enough.
It seems to me that any question asking for a word or phrase for a given idea may have multiple answers, whether or not there is variation between dialects. There are of course many questions of this form. Take as a single example from recent questions Is there a word for a non-geek? Many possibilities were suggested. The list may or may not be complete, they are not all in a single answer, and it's difficult to tell whether there's a single best one. I still find it constructive.
Imagine the OP had simply posted a picture or description of the hat, and asked what it was commonly called, without mentioning dialects or soliciting individual regional answers. It would be extremely similar to a multitude of questions on the site, would have gathered the same sort of information in its answers, and if the terms vary from region to region, that would have been mentioned in the answers. This suggests to me that the core question is quite valid. Given that the OP expects some variation between dialects, it seems reasonable to include that information in the question, so that answers are more likely to consider that. It also seems preferable to ask as a single question first, rather than simultaneously posting one each for the major dialects.
So to me, it seems that the first action for high-rep users upon seeing questions like this should be to encourage editing (and vote to close if the question is currently in a very bad form), or even just edit immediately, rather than giving in to the "close and move on" instinct.