The only case I could really find where it makes a difference is in slow and smooth colour gradients on which you can see the increased precision. However, that can also be basically solved by adding (rand()-0.5)/255 to all fragments before output.
The increased brightness kind of doesn't matter since SDR content is usually just stretched to fill the increased brightness range.
The most interesting thing for me was the wider colour gamut that you get with the rec2020 colour primaries. Unfortunately I couldn't really reproduce anything looking actually different, let alone better.
I was doing my lighting in the rec2020 colour space, and I was producing out-of-gamut colours for rec709, so I really was seeing colours that SDR content would be totally unable to produce. Yet somehow my eye just couldn't preceive a difference when switching back and forth between the two images.
I am using an LG OLED which are supposed to be good for HDR so the display shouldn't be the issue.
I would be keen to see some references that really quantify the difference between HDR and non-HDR rendering where the HDR version doesn't just look darker.