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I don't understand why the postulate of "Energy Quantization" is needed to explain the black body energy spectrum.

I think it suffices to say that Energy is proportional to frequency. That statement alone, taken together with Boltzmann distribution, implies that there will be less energy present at higher frequency. And this explains why the black body radiation spectrum dies away at higher frequencies. Why do I need to invoke quantization?

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Energy of what is proportional to frequency? Of a frequency mode. This is already quantization because if the mode energy is proportional to the mode amplitude, it can be anything.

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I think it suffices to say that Energy is proportional to frequency. That statement alone...

is either (a) not an actual dynamical statement, or (b) inconsistent and prima facie impossible.

There are plenty of different electromagnetic modes, each with its own frequency $f$ - that's just the playing field. If by that statement you mean that the energy that each mode holds must be given by $E=hf$, where $h$ is some fixed universal constant, then your formalism does not allow for the energy spectrum to change if the conditions of the system (say, the temperature), which is precisely the problem you were trying to solve (i.e. how does the energy spectrum depend on the temperature).

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