The problem with the italicized portion is that we don't know to what extent a notion of "actual behavior" may be meaningful, if at all.
That's correct, we don't. But even then the problem of conflation, described in my 3rd point in the previous post, applies. But with a positivist slant, where "actual behaviour" translates better into "actually observed behaviour" or something in the same vein.
An enormous amount of ink has been spilled on the question of "elements of reality" (terminology commonly attributed to Einstein), which today might be called "hidden variables", with the eventual result of the vast majority of physicists regarding the problem as hopeless and working on something else. The mystery is not in interpreting the quantum state as a recipe for calculating probabilities of experimental outcomes; that's straightforward. The mystery, for those who see a mystery, is that nobody's been able to come up with a classical statistical ensemble that's described by the quantum rules, and not for lack of trying.
Indeed, a consideration which I also tried to weave into my 2nd point in the previous post.
I'm not sure what you mean here. Take the example of the classical Brownian particle: it has a well-defined position at all times.
Right, I'm not disagreeing with the overall point that it's important to avoid mistaking the model for the physical system, and that many routinely do, and that doing so is a big source of confusion. But at the same time it's not "just" classical stochastic behavior and the fact that measuring small things is hard.
This is correct (that it's not "just" classical stochastic behaviour) in terms of the specifics, but not in terms of the general idea of propensity probability (a sort of 'guided' stochasticism) which exists also in other fields and which was discussed under the 1st point of my previous post.
That's the case with the amplituhedron. It seems computationally advantageous to calculate scattering amplitudes by just computing the volume of some polytope instead of adding up Feynman diagrams and keeping careful track of the many cancellations that come with N=4 super Yang-Mills' highly supersymmetric structure, but that's assuming you want to calculate scattering amplitudes in the first place. There are other questions to be asked of a particle theory, and for other questions the perturbative diagrammatic approach may be more convenient.
The amplituhedron is not just about computational benefits to calculate scattering amplitudes. Besides, by so stating you aptly captioned the main disconnect in the way the entire project of science is understood between many (not all) quantum physicists and 'classical' physicists; Namely, 'computational advantage' in predicting observations, as opposed to 'understanding physical reality' underlying observations (i.e. Bohr's positivism vs. Einstein's realism).
Be as it may, it's my understanding that for Nima Arkhani-Hamed, his collaborators and those most impressed by his discovery it's more the potential which similar geometric models could have in describing gravity, and to account for the existence of particles, and the spacetime, in the first place. His project is therefore far more ambitious than particle interactions. It's about discovering a more fundamental math underlying and unifying all physics. Which may or may not succeed.
Unless and until quantum physicists, on the whole, gain a deeper understanding of n-dimensional geometric function spaces (which they usually know zilch about), they do not yet have much say in the potential quantum mechanical applicabilities of models like the amplituhedron. Which brings us back to the matter of inadequacy of currently used language raised in the OP. Indeed, it would be a formidable task for a non-Arabic-speaking evolutionary biologist to comment on, let alone to correct, an Arabic-speaker's lecture on the topic.