In terms of why you can't just build your own matrix? Well, at any given pixel representation you have to not only decide what size dot (if the printer has variable dot sizes) of each colour and its placement to build that pixel representation, but also how it affects the representation of the colour pixel next to it (which means all around it), and to minimise metamerism and so on. The LUT that the printers have available in terms of matching combinations to achieve not only the individual pixel representation but also the total effect of all the represented pixels is huge. It's in the hundreds of billions of possibilities. Then it depends on the output resolution you want (trading accuracy against speed), whether you're printing uni or bi directional (again accuracy with speed), considering the media and the drying times and so on.
If you open that up to "any matrix you like" means not only increasing the combinations and the processing needed to render that image, but also an expectation that users know what the impact is of changing the matrix. It also impacts on the physical precision and movement of paper and print heads to achieve those results and, if there's a print quality issue, the problem of trying to diagnose whether it's the custom matrix or something else doing it.
Jim's article addresses some of these complexities, but I think it misses the vast amount of data involved in the LUT for the colour decisions. The more variables, the bigger that becomes and the more choices that need to be made. And, most importantly, where is the evidence to suggest that the current iterations aren't already quite optimal compared to others that might be proposed? In other words, if you allow change, what is the return on investment? How much better (if at all) would a print be compared to the cost in time, money, computing power, and so on?
Even RIP vendors don't venture outside of these realms, and if you have seen the time taken to RIP large images on even the fastest hardware you'll realise that it's still processor intensive and produces very large rasterised image files.