There is a story about Gauss being "unimpressed by FLT, pointing out (after finding a proof of the n=3 case) that in number theory it’s very easy to come up with problems that are very hard.".
But, it is known that there were many developments in number theory since the time of Gauss, and some of them were needed to settle FLT (I am not implying that Fermat did not have a proof, an "elementary" one, but the margin was too small).
Also, the conjecture of Goldbach surely was out of reach in the time of Goldbach and Euler, but today it stands as an important problem in the theory of additive bases, in the subfield of additive number theory.
Therefore, I am of the opinion that a "good" mathematical question, no matter how hard, could be a source for a new developments in the field, and, possibly, for some future applications, outside or inside the field itself.
Because of that, I am of an opinion that questions that generate interest and are hard should be encouraged, and should not be closed because closing of them discourages a person who asked that question.
Also, importance of a question and its impact on the field is very subjective matter, and, what to someone seems as just another question, to someone else could be a source of inspiration for a lifelong study.
So many of us are able to ask questions that are hard, but this question is more about non-professionals than professionals, for example, I, as a non-professional, must think so much about some topic to hopefully arrive at a question that could interest some of you, while many of you can in a fraction of an hour ask a couple of questions that are very hard and, maybe, non-answerable with current techniques.
Because of that, I think that it is recommendable that some of non-professionals actively participate at the site for professionals, and that they ask questions that are hard, not just hard but also those that are very hard (if possible), because, a smart question, no matter how elementary in its formulation, can generate so much of research and can be a source of new developments.
From all of this I would also like to add that I do not like the politics of putting questions "on hold", or "closing" them, just because they are elementary in formulation and very hard or hard or at least complicated to settle.
Here the rule "the harder the better" can be applied, not because of our present inability to settle some questions, but because of enrichment of the field itself.
As about me, I am more of a conjecturer in mathematics than developer of mathematics, but the act of making conjectures in mathematics and of developing the field cannot be separated, they are very intimately connected.
Also, I think that professionals should offer as much help as possible to non-professionals, if the intentions of non-professionals are good, because it is possible that some non-professional becomes a professional, but without help, it is possible even without help, but it is hard if there is no help at all.
A conclusion would be, that:
Non-professionals should be encouraged on this site if they ask a question even if it is elementary in formulation, and that generated a discussion, but did not receive an answer that settled a question, and that question should not be put "on hold" or closed, if it was asked in a clear and systematic way.