The ImageMagick “-hald-clut” operation changes each pixel in an image by looking up the colour in the HALDclut image, which is conceptually 3D. It does a 3D interpolation, not a simple nearest-neighbour, to calculate each output pixel. Hence I don’t think there is a lack of precision with the method I showed. (But it would take more time than I have today to demonstrate this.)
ImageMagick doesn’t have G’MIC’s powerful ability to manipulate (including resizing) general 3D images.