Dear Dr. Wlodarz:
Your essay is very concise and very clear. Mathematical models work because they are designed to do so.
I agree, and my own essay, "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory", focuses on a particularly egregious example of how an incorrect mathematical model became accepted as reality, despite obvious "paradoxes". I argue that contrary to universal belief, a simple realistic picture of the microworld is possible, completely avoiding the paradoxes that plague orthodox quantum mechanics (including entanglement). QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains similar to solitons. This requires nonlinear mathematics that is not present in the standard Hilbert-space formalism. This also makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.
So while mathematics can provide important insights into physics, an incorrect mathematical model that becomes established may be seen as virtually religious dogma which is not to be questioned. That prevents further progress.
Alan Kadin