There is a mathematics-education tag with $187$ questions asked; more strikingly, there is a soft-question tag with $931$ questions asked, and the wiki-description of this latter tag is: "Questions that ask about some aspect of mathematical research or study which doesn't involve the actual mathematics. In general, soft questions can be answered without using mathematical reasoning." My feeling is that Mathematics Education questions are about an aspect of mathematical study, and often don't involve (research-level) mathematics, nor do they require the sort of reasoning common to graduate programs in pure mathematics.
Perhaps also of interest is searching for the word favorite: there are $802$ results. The results vary from What are you favorite instructional counterexamples? to What are your favorite puzzles/toys for introducing new mathematical concepts to students?. (The latter includes the teaching tag, for which there are $137$ questions asked.)
It seems to me, then, that a question such as "When did you first encounter the idea of problem-solving heuristics (cf. Polya) and has it affected you in your own problem-solving?" is quite reasonable. Answers to these questions from experts (i.e., professional mathematicians) are valuable, at the least, to Mathematics Educations researchers (some of whom include professional mathematicians). I should think that mathematicians would be interested in improving the state of Mathematics Education, and that MO is an excellent place to get the sort of expert answers one could not find elsewhere. I realize that the italicized portion in my previous sentence does not in and of itself justify Math-Ed questions; nevertheless, I am quite confident that an education-overflow site would not do justice to Mathematics Education in particular.
Finally, I agree with a remark made by G. Kuperberg (though I don't mean to imply he would support my position here) within the highly-voted post on the Philosophy behind Mochizuki's work on the ABC conjecture. In a comment, he observes: "I think that people are working way, way too hard to define MathOverflow by what it isn't. Although I still like MO, too many babies have been thrown out with various bathwater." Pure Mathematics is different from Mathematics Education; it is also different from Applied Mathematics, History of Mathematics, Mathematical Modeling, Statistics, and so forth. Which of these should stay and which of these should go? Here I respond only to the MSC $97$ query, and say: If others wish to define MathOverflow by its avoidance of Mathematics Education questions, then I am disappointed. I think that pedagogical questions - like historical questions, etc. - can be phrased in a way to make them appropriate for MO.