You are wrong and the proof is simple. Take the color control on any projector to zero. What does yellow look like? It will look very light gray not black.
Saturation is being changed not intensity/lightness.
No, I'm not.
Your results with yellow are easy to explain. Of all the primary and secondary colors, yellow has the highest intensity, over 90% of reference white. Color controls have a limited range of adjustment. Try the same experiment with blue, which has the lowest intensity. You'll get the black you were looking for.
All this demonstrates is that the Color control doesn't act like a perfect Contrast control (something I never claimed) and that lowering color intensity also lowers saturation (something I never denied).
Let's perform a more serious experiment. Here's the Rec. 709 standard for red.
The xy coordinate defines the saturation and hue of red and places it on the CIE chart. The Y value is color intensity and is not represented on the CIE chart, except indirectly because Y affects saturation. The xy numbers are fixed coordinates. The Y value is a percentage of reference white. Thus, a red that is properly intense will measure 21.3% of the luminance of reference white. You can measure this with a standard light meter. xy coordinates can only be measured with a colorimeter.
Your claim is that one should use the standard Color control to lower oversaturated colors to their proper place. My claim is that you CAN do this, but you shouldn't, because the primary component affected by the Color control is Y, not xy.
How could we test these competing claims? It's simple enough. Just measure the xyY of an oversaturated color and then progressively lower the Color control and see what happens.
I did this with red. Here's the original CIE chart from a digital display. I'll be happy to repeat this experiment on an analog monitor.
The xy coordinates are 0.669, 0.322.
The Y is 21.9% of reference white, very close to the target of 21.3%.
Here are the results as the Color control is lowered.
Here's the CIE chart after lowering the Color control 17 ticks.
OK, now we have achieved the stated goal using your recommended method. The xy coordinates are nearly perfect. Red is no longer oversaturated. But look what's happened to Y! It has gone from 21.9% of reference white to 12.0%, a drop of approximately 43%. In other words, a modest improvement in saturation has cost us nearly half of the intensity of the target color. This has disastrous results for the quality of the image.
Do NOT use the Color control to adjust saturation.