I tend to try and be a realist in these situations. What would you see with the naked eye? Certainly nowhere near as much as you've recorded in the very first image. Too much would be in silhouette and yet we accept this because that's just how life is.
Could you improve on the MkI eyeball? In a way, yes - but only by shielding your eyes from the strong light surrounding the chopper. What would that give? Overexposed (blinding) sky, with no detail in the highlights but the opportunity to see the shadow detail will be there. Why does it work in real life? Because the brain sorts out what it wants to try and see, excludes or ignores what it doesn't want to record.
The photographic record can't perform this trick of selection so we see through this imagery everything or nothing. So, at best, what we have is a compromise between highlights and shadows. And that has been the case since Fox Talbot recorded that window at Lacock Abbey!
HDR can be good in some cases, but certainly not all. Too much looks unnatural .... IMHO