I've never been as impressed with the hierarchy problem as many (most?) theoretical physicists seem to be, but I think that Nima Arkani-Hamed has his the nail on the head in describing in general terms what is going on: "The solution to the hierarchy problem involves a completely novel mechanism." We have not, however, figured out what that mechanism is yet. Arkani-Hamed focuses on two approaches, neither of which have worked so far:
One is based on trying to apply notions related to self-organized criticality, but he was never able to make much progress.
Another is based on an idea of Ed Witten’s that perhaps our world is best understood as one that has:I am unimpressed with the second approach (Arkani-Hamed hit a pretty fundamental dead end in trying to square this with the Standard Model reality too), and don't know enough about the first to comment (the link above is suggestive of the idea but doesn't apply it to quantum physics). But, I do think that the bottom line, that their is a mechanism or perspective that makes the seeming unnaturalness associated with the hierarchy problem seem natural is correct.
two dimensions of space (not the obvious three);
is supersymmetric(which seems impossible, but in three dimensions supersymmetry and gravity together imply that particles and their superpartner particles need not have equal masses);
has extremely strong forces.
In my view, the hierarchy problem is an issue of defective framing, category error, or failure to appreciate a key relationship between parts of the Standard Model, rather than anything that should surprise a physicist who knew the whole story.