Constantinos,
In your reply to Jose you state, "The issue here is not whether we can derive Planck's Law 'with or with-out quanta',"
I see your point. While substituting eta in your equation for h in the derivation you use of Planck's Theorem, does have the exact form, it is not the same mathematical identity. Which I think is your major argument.
I have not found the derivation you employ in several references I briefly looked into but accept it as it is quite apparent you are very familiar with the vast body of work which has developed from his original formulations. Let me start there because I'm quite content with the simple reductions and think the derivation is good as it simplifies to an energy term on the left side. (And I really don't have the desire for a lot of math)
In essence, and I think this is important in how you introduce others to your work, what your identity does is to make global what is expressed locally to the incident waves from a source by the Planck identity. And more. It is scale independent, by averaging the energy term it can show the local value of h as the absolute value of a single wave event to be a time dependent action, while also extending relativistically to infinity. It was the limit at infinity that had me worried.
So in real terms and applications your equation is complimentary to Planck and does not displace Planck's (theorem) Law. And it can't without also refuting the basis of itself. Nor would many accept doing away with its reduction to e=hv.
Another aspect of the global feature is that it might be applicable to a 'flat flow' measurement. If you are familiar with mechanical maintenance and how an AC Induction Motor operates, the characteristic of 'slippage' gives a good illustration. Without digression in how its done, the magnetic field in the stator electromagnets rotates while inducing magnetic field regions in the rotor. But the rotor's physical rotation continually lags behind the stator field rotation, its 'slipping'. Now consider the slippage cylindrical plane as a flat wave. Similar to the shear plane of laminar flow in hydro-dynamics. Its not that the slippage doesn't give a perturbative reactance in producing an electromagnetic field, it does and its scale independent, you can hear it because to rotor's speed produces oscillation in the audible range.
In your paradigm of interaction of measurement as mathematical identities, that slippage illustration could possibly apply to a continuous flow through the medium of an emitter source. Interactively, evanescent waves which are those that reflect back into the interior of a medium, decay exponentially in intensity. That could be related to your 'if the speed of light is constant, light is a wave', and the interface at emitter and absorber.
So I think you can say that whether I recognize it or not, I'm responding in accord with your hypothesis that it is mathematical identity by which we do physics. Don't expect to purge physics anytime soon of it being used to discover 'what it is', that's why most people go into physics instead of math.
Cordially, jrc