Let me debunk one thing: "RGB and CMY are two different color models."
They are not, they both form part of one RGB-CMY model. Or probably an RYGCBM model.
Ok. That is not entirely true but in essence yes. On one model 3 are primary and the other 3 secondary and vice-versa.
Look at any modern color wheel all 6 colors are present. Some models are dimmer and less saturated because they are simulating the capabilities of the final output, but they are all there.
Some color wheels do not have black or darker colors, because a color wheel is in reality the top view of a color solid. I use the word solid because they can be many shapes. Cubes, cylinders, a double cone, spheroids...
CMY(K) image requires to be illuminated by white light.
That is the full point. Where does the light come from? Do I start with the full spectrum, do I need to add more and more light, different wavelengths? or I need to remove them.
Historically it is easier to remove the light. That is simpler. Any colored material does that.
When a printer performs printing operation, how do CMYK and RGB work together to print on white paper?
They work together because they are all part of the same color solid. But it needs to have a conversion because one is based on some primary RGB and the other need to use CMY as primary colors.
Allow me to spam you with an old webpage I wrote some time ago. I am sorry that it is not in English, just take a look at the image.
A basic conversion is just taking one channel and using it as the complementary color. Take the R channel and use it to print C ink.
But why? Imagine you have on your Red channel some black zones that have no red, that is why it is dark on the red channel.
That means that you should print a lot of Cyan because Cyan has no red.
Let me simulate this.
On an RGB image, I am breaking the RGB channels into a grayscale image.
We can identify each one compared to some clear color zones, Red ballon translates into a bright zone on the Red channel. The same with G and B.
If I use those channels as the complementary color directly I could still have a decent color reproduction. The image on the bottom left is a reference image.
Why is CMYK more efficient/beneficial than RGB for performing printing on paper?
I think the next examples are not what you asked, but let me explore.
Ok. Let's try not using CMY colors, but RGB. These are red, green, and blue inks, using the exact same channels as the RGB file.
Hum... we have a mess. We have what we asked for. The cyan water is black on the red because we do not have red on the water. But now we have a lot of red because of the black of the ink red channel.
Ok, how about using some other colors, not RGB, nor CMY... how about the colors used traditionally on the RYB color model, before the magenta dyes were invented. The blues were also less cyan-ish before the cyan pigments were invented.
We could live with that. We also could have brighter reds.
The first answer is, we use RGB when adding light, and CMY when subtracting light because adding is the opposite of subtracting then
we use the complementary color.
And why does CMYK technology need... white paper
Try starting with black paper and transparent inks... Not good. What do you want to reflect with your print if all the light is already absorbed by the paper?
In the end, the question is, can your object emit light or only can reflect some light that comes from somewhere else.
Returning to the question
Why is CMYK more efficient/beneficial than RGB for performing printing on paper?
If you are referring to a CMYK file instead of an RGB one the answer is just that, in some controlled environments you need to define the exact amount of ink of each channel, therefore you need to save those values on the file itself, then, you need a CMYK file.
Each combination of ink-paper needs different values of ink. That is what a color profile does.
On a home or office environment, and with the humungous amount of color printers, you let the printer driver make the decision on how much ink to inject. That is why is preferable to use an RGB file. Let the driver drive the conversion.
In commercial print, you follow some standards. Gracol, SWOP, European, etc. With standardized inks on standardized papers. So you define one specific conversion and save it on a CMYK file, so the values are fixed for that particular case.
Ballon image.