The reasons why are interesting, but it has to do with how the eye processes images and color.
Remember, you can turn your screen as bright as you want. But it doesn't help the content appear more "real" or "better" or "HDR-like". Therefore, HDR is simply "the ability to discern between different levels of color." And if you try to measure exactly how many levels of color a human can discern, the answer is no more than the 256^3 available via 8-bit RGB.
The precise claim: if you have two screens next to each other, one 8-bit RGB and one 10-bit RGB, and both screens are color calibrated / brightness calibrated identically, and the viewing conditions are identical for both screens, then if you blindfold someone and put them in front of a random screen, they will be unable to say "Ah, this is the 10-bit RGB screen!" more than random chance.
10-bit also comes with much better calibration precision where the translation isn't done in the display itself.
I didn't say to turn down the brightness of the HDR screen. I said the brightness per area must match.
Using maximum brightness often harms color reproducibility too, by the way. So if you believe brighter = better, don't.
But that’s not what HDR is. 8bpc is definitely not enough to represent HDR Rec.2020 or DCI-P3 without significant banding.
Because 8 vs 10 bit colour in sky photography is quite obvious