Then why do you keep disagreeing with it and making stuff up?
Again, you are the one making counter-factual claims. It is up to you to support it.
But...
One of the first things that made Planck realise that electromagnetic radiation is quantised was the black body spectrum. This is continuous (analog, as you put it) and the equation includes Planck's constant. So Planck himself proves you wrong:
[math]\displaystyle I(\nu,T) =\frac{ 2 h\nu^{3}}{c^2}\frac{1}{ e^{\frac{h\nu}{kT}}-1}[/math]
What is the point of a compromise, when you are wrong.