Are you sure that the purpose is not to return it to a known and repeatable state, which is not necessarily a specific original state or standard? If that were the case you could use any of the 17 recommended papers to get it back to that original state and it would not be necessary to always use the same paper when you calibrate, since they would all calibrate the printer to the same state.
It makes sense to me that the printer will calibrate itself to a slightly different state, depending on which paper you use to calibrate it with. And that then is the reason to always use the same paper, so the printer always goes to that state and remains consistent. It also makes sense then that if you want two printers to print exactly alike, that you calibrate them with the SAME paper, so that they will go to the same state.
Yes, I would say standard or known repeatable state rather than original, as the printer cannot be factory tested without printheads installed. You set the standard state with the initial calibration on paper you will keep for this procedure in the future. I don't understand why Canon doesn't just specify the single supplied paper to be used, though.
If you are unhappy with prints from stock profiles, and have eliminated monitor cal. problems by printing an unmodified printer test image that is "off" in the same way your own files print, then custom profiles for your various papers should solve the problem. I've not found this to be the case over 8 years with several iPF's, though.
Pete