As noted at the beginning of your article:
"The principle of linear superposition...Along with the uncertainty principle, it provides the basis for the mathematical formulation of quantum theory." You then suggest that it might only hold as an approximation.
I view the problem rather differently. Fourier Analysis is the actual mathematical basis for quantum theory. Superposition and the uncertainty principle are merely properties of Fourier Analysis. In other words, they are not properties of the physical world at all, but merely properties of the mathematical language being used to describe that world. Even the well-known, double-slit "interference pattern" is just the magnitude of the Fourier Transform of the slit geometry. In other words, the pattern exists, and is related to the structure of the slits, as a mathematical identity, independent of the existence of waves, particles, physics or physicists.
For the better part of a century, physicists have been misattributing the attributes of the language they have chosen to describe nature, for attributes of nature itself. But they are not the same thing.
Fourier Analysis, by design, is an extremely powerful technique, in that it can be made to "fit" any observable data. Hence it comes as no surprise that a theory based on it "fits" the observations.
But it is not unique in this regard. And it is also not the best model, in that it assumes "no a priori information" about what is being observed. Consequently, it is a good model for simple objects, which possess very little a priori information. On the other hand, it is, in that regard, a very poor model, for human observers; assuming that it is, is the source of all of the "weirdness" in the interpretations of quantum theory.
Putting Fourier Analysis into the hands of physicists has turned out to be a bit like putting machine guns into the hands of children - they have been rather careless about where they have aimed it. Aiming it at inanimate objects is acceptable. Aiming at human observers is not.