perhaps the degree of quantization is so small the radiation curves look continuous
Yes, this is the reason. The correspondence principle says that quantum mechanics has to become classical in the appropriate limit. One way to obtain an appropriate limit is with large numbers of particles. As you increase the number of particles in a material many-body system, you get more and more ways of putting together combinations of states for your material object. The density of states of the object grows very quickly (roughly exponentially) with the number of particles. Therefore the number of possible transitions between states also grows very rapidly.
The number of particles in a tungsten lightbulb filament is something like Avogadro's number. The exponential of Avogadro's number is really, really big.
Well, you are mixing things in your question, you say:
. I'm just curious to know the proper historical development of this non-trivial fact of reality
This is historical:
The Nobel Prize in Physics 1921 was awarded to Albert Einstein "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".
No semiclassical explanations at the time , because the link you give is not historical, it is decades after the detection of the photoelectric effect and its interpretation as the photon being a discrete particle.
You yourself give the historic path.
Now there is a solid quantum mechanical theory called the standard model of particle physics, where the photon has its niche as a point particle on par with electrons and neutrons in the Lagrangian .
This model has been validated by innumerable data, and the chase for physics beyond the standard model goes into making photons into string excitations, not continuous classical electromagnetic waves.
Now wavepackets, that your first reference states, are necessary in the Quantum Field Theory of describing nature, which works with quantum "events" in effect. So I do not see anything revolutionary:
Do we count indivisible photons or discrete quantum events experienced by detectors?
One could ask this for all elementary particles, and certainly they are quantum entities, not classical particles .
Certainly there are hundreds of other historically important papers that are going under the rug here
Do you have any links? I do not think they exist, which is the reason Einstein got his Nobel.
In conclusion, any semiclassical arguments have to face all the bulk of data of the self consistent current model that describes particle data, i.e. embed them in the new format, because these are data too , in addition to the photon being an elementary particle.
Best Answer
This link gives a clear account of the difference between the classical and the need for the quantum mechanical formulation .
Continuing perusing the link you will see the justification of the classical formula and the fact that the data does not follow it but follows the quantum induced formula.