Could you identify what you think I'm overlooking?
Ok lets perhaps start with what you said here:
For instance, the scanners are capable of giving sRGB jpeg output. With proper printer and paper profiling, I should be able to get relatively identical results with any printer that supports ICC profiles, since the properties of the sRGB color space are well known.
Lets just for a start deconstruct this, except lets further simplifying it by discussing pure digital photography straight to screen and to a printer.
When you capture a photo with your DSLR the voltage created at the sensor which then becomes a number results in numbers that have a linear relationship to each other. For example a value of 36% is very close to twice as intense as 18%. (18% being roughly midscale in perception). (If the camera was perfect then 36% would be exactly double of 18%) The spectral sensitivity is carefully designed by the manufacture so that a colour matching function can then be used map those values to CIE XYZ or any other known colorspace. After capture the photo can then be processed directly in the camera to JPG, or you can do it with something like lightroom. The order of the steps is very similar, and the order DOES matter.
For example after demoscacing your data, you must first move the camera data to the new target colorspace, lets say you have chosen sRGB, so you must apply at least one forward matrix to move from camera colorspace to sRGB. Then you can apply the sRGB gamma function and then a tone curve (chosen by the manufacturer) to give the desired result.
Now at output stage the display hardware either by using appropriate phosphors in your CRT which match the primaries of the sRGB standard and using properties of the electron gun in the tube as the standard was envisaged to remove the sRGB gamma. Or you can use modern LCD or printer which remove the sRGB gamma from the signal and remap as appropriate, and apply an appropriate matrix/LUT to match the spectral qualities of the display or inks. The result after all this will still leave the tone curve that was added for pictorial reasons and any additional colour tweaks that are added by the manufacturer. That will distinguish one camera from another etc etc. Unless of course you believe all cameras are the same...
There are two points to make in this example which is broadly correct for illustration purposes. The first point is you can reorder a few things, but hopefully you can see that if you reorder things in the wrong way either the maths becomes very complicated or does not make sense or you get a different result...
The second point which is probably the most important is that there are something things in this pipeline that are added and then effectively removed so the net result is it makes no difference, leaving the manufacturer colour and tone tweaks...

For example if your colors fit in the sRGB colorspace then it is as if didn't exist, otherwise it either clips them and you loose a few or it change all the colour slightly to fit the colorspace. But it doesn't change the signature of image, i.e. the tones and the general appearance of the colours etc. The manufactures tone curve and colour tweaks do!
In the discussion of colour negative films previously, hopefully you can see that there are several things in the camera negative, that "magically" disappear in the print, and leaving both the colour and tone "signature" designed by manufacturer. Keeping in mind the choice of print stock will vary the final result (there are still a handfull to choose) and also the exposure of both the camera negative and print will also vary the result. Many rate 400iso films at 100 or 200 etc. But there will be something that our brains can certainly distinguish.
Now after this long explanation if you profile as you describe with your 288 patches, how will you distinguish the characteristics that disappear when you print the camera negative from those that should be there which are the "signature" of the film?
What I think your are overlooking is that your modelling must consider at least part of how film works so that it contain at least some of its inherent characteristics. Otherwise you will remove all distinguishing characteristics from the film.
Hopefully this makes some sense!
