What looks "real" to the average viewer
HDR aggressively applied looks weird to some of us now, but will it always? Black skies with violently processed fluffy white clouds are the thing, these days, and some people like them. Now, I think these people like them because the effect is eye catching, and they specifically like the effect. Will it some day be normalized, will the over processed look appear normal, so we see only the image, with a lot of visual drama, not the processing?
In any photograph, we're forced to mentally edit out an enormous amount of artifice to see the "real" image, see this post, for instance, and there is no reason to imagine that as new approaches to rendering come along, we will not learn to edit those out as well
There is an Overton Window effect in play here, however. At any given time there is a range, or a general "region" of renderings which will feel natural to the viewing audience. This window does move over time, as any cursory investigation into historical photographs will clearly show. If your goal is to make photographs accessible to your viewers, you should respect that window. The overlooked black skies may soon enter the window, and indeed for some more modern viewers they may be in-window now, but in my judgement the general viewer is still seeing the processing. Rendering skies as pure white, in the style of the 19th century, is also out of the window, albeit the other way. At this point we're pretty much expecting a late Ansel Adams look to the sky, and you can probably push that a bit. But, not too far!
Will violently applied HDR ever enter the window? I cannot help but hope the answer is negative, but the choice is not mine to make.