I can tell you there are some places people do notice that a screen can't reproduce all the colors they can see.

Anyone who has mixed paint at hardware store or paint store with a modern paint machine will eventually notice this. A of lot them have a spectrometer to match color from a sample. The software often has a preview that appears on a screen of the sample color. That preview color is often not quite the same and it's often either the limit of the sRGB color space or the monitor.

The data from the spectrometers is eventually converted to CIELAB color points with a D65 white point. Then that little preview needs to be converted to sRGB to display it or some colorspace the system supports.

There also some problems with the LAB colorspace, but they are minuet compared tot the limits of sRGB and display hardware.