Also, you have to consider the reason for the 4th channel. CMYK inks are transparent, so 100% CMY is never close to absolute black, and there has to be the extra black plate in order to get a believable black appearance on press. That means there is a lot of redundancy in different 8-bit output values, which produce the same color appearance.
In this example we can see the GRACoL profiled CMYK channels are showing two very different CMYK output values, 58|38|14|1 on the left and 42|25|2|20 on the right. However, my #3 and #4 color samplers show that the colors have the same appearance assuming the press runs exactly to the GRACoL profile—their Lab values are both 60|0|-20:
