It seems that the software is doing a negative film photographer's trick of "expose for the shadows and the highlights will take care of themself" but rather it's "expose for the shadows and the HDR will take care of the highlights" - ending up in this overprocessed looking fake sky effect.
It's like there can't be any ambiguity anymore in a photo due to the exposure, the shadows and the highlights can't clip, we have to see everything. That seems a big change in mindset to me.
A painting of a room with a window would typically show both the room and the scene from the window "perfectly exposed", like the iPhone is doing with your skies.
This looks very strange to someone used to images from more traditional cameras, and the artefacts like halos stand out.
Oversharpening is a curse in the industry to be sure, unfortunately to most people an oversharpened image looks "better".