That's a good question, and the simple answer is that while the display screen may have a 'linear' response to a change in input signal, very few in-built display colour management systems are themselves 'linear'.
This means the display's cms will introduce non-linear inaccuracies.
Unfortunately, this is all too common.
Also, the granularity of a 3D LUT is far greater across the full volumetric space than any display cms.
(Basically, in the example on the website page you have 17 point control over Red, Green, Blue, and Grey Scale, with the volumetric correction calculated between them - that is just no possible with basic display controls).
That will always produce a better final calibration.