Just look at the PQ curve. It is very flat at the bottom (almost SDR gamma 2.40) and then rises rapidly when the brightness increases. The SDR gamma curve can't replicate this brightness response. That is why the HLG curve was invented. SDR gamma was also replaced with PQ and HLG because tests found it leads to banding when the brightness range is stretched too far.
If you want to test if your display is handling color correctly, download the
Life Untouched 4K HDR Demo.
Find this scene and observe the color of the flower petals:
Flowers Correct Hue
Flowers Incorrect Hue
If they are blue, there is a fair to good chance your display is handling color correctly. If they are purple, your display is probably shifting some hues.