Inquiring minds want to know... where else in physics do we find application for the equivalence principle? Of the top of my head I can't come up with anything but gravitation & rotational frame of reference.
I can't either, but it should be noted that it's just a particular example that's especially relevant to the OP because the question was initially gravitational. The general situation:
The view of science that quantities which you cannot discriminate with instruments are the same thing is about the only philosophy of physics which has been definitively discredited in the last hundred years. So it is rather inappropriate to try it on here, don't you think?
denies that observationally indistinguishable things should be taken as
fundamentally equivalent whenever possible. I can't read this as anything other than a straight-up denial of Ockham's razor, which would be used (for example) whenever there was a theory unifying phenomena that were initially thought to be disparate (in the case of the equivalence principle, this would be gravitation and inertia).
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As near as I could understand, the philosophy objects to it because it defines physical things in terms of measurements. For example, the length of something is defined by the time it takes for light to cross it. The problem being that we can also measure length other ways, like by using a ruler. So we apparently have defined both "ruler length" and "optical length", without allowing for an underlying "true length" that both measurements are supposed to be equal to.
I doubt that even deserves characterization a philosophical argument. There is an operational definition of a unit of length, so the former would be the "true length", while the alternative and easier methods, such as rulers, would be approximations. This is straight-forward even by standards of philosophy.
Somehow they went from "real things must be measurable" to "models are useless", pointing out things like how you never directly measure wavefunctions, or the thought experiments Einstein used to come up with relativity.
Wavefunctions are just as measurable as position, momentum, energy, etc.--i.e., in just the same sense as anything any other observable*. In the position basis, its amplitude-squared is a probability distribution of position measurements, and thus measurable in the statistical sense over many identically prepared particles (i.e., not conceptually worse than any other observable), while its phase of the wavefunction represents the probability flux, which is empirically recoverable from measurements over different times.
As for Einstein's thought experiments to argue something like that, I don't see the point, because what they did was ultimately the exact reverse of what that person is arguing for (i.e., the equivalence principle treats observational equivalence as indicative of fundamentally identical phenomena).
[size=-1]* In QM's language, the |ψ(x)|² is the expected value of the projection operator to the eigenspace of the position operator with eigenvalue x. Since this operator is self-adjoint, it represents an observable.[/size]