The reason for doing this on input is to prevent the math from breaking early in the pipeline. Specifically, if this is not done, in many cases the matrix that has the closest compromise fit leads to bogus negative luminance values in XYZ space when the camera is seeing a strong blue input (such as a blue LED).
The gamut compression is effectively undone using the 2.5D LUT in such a way as to not wind up with a negative luminance in XYZ space, which is why it is done as part of the input profile.