For smartphones, where thinness is very important but area is less so, it would not be unprecedented to make an array of 4 monochromatic cameras and rectify and combine the images computationally.
Unfortunately, that is not how light and perception works.
There are thousands/millions¹ of separate visible light frequencies. Our eyes and brains takes that all in and does an enormously lossy mapping of that to 3 perceived colors.
If you only record 3 of those thousands/millions of frequencies, you will lose 99.9% of the light, and mostly make black photos.
¹ depending on how wide the frequency interval considered monochromatic is.
Cone cells have fairly peaked frequency responses, and due to random projections caused by the cascading, this is sufficient to fully reconstruct the signal, i.e. the converse of the statement is true, you can retain 99.9% of the perceptual information using 3 sensors, all you need is to perceive in time and some randomness in the sensor placement.
They're not really that peaked, the M and L cones largely overlap, even, and are spread over at least a third of the entire visible spectrum. Pictures at: https://en.wikipedia.org/wiki/Cone_cell
You can maybe retain 99.9% of the color information humans can perceive, but that is a very small part of what's in the visible spectrum signal.
Maybe this example will clarify: Our eyes can not tell the difference between monochromatic green light (540nm) and a mix of blue (470nm) and yellow (580nm) light.
That only says something about the display to eyes end of things. If you record only a subset of the visible spectrum the image can end up wrong. You might actually not get any color at all in the worst case.
The original poster was much more apt than your explanation. CMOS sensors in modern cameras actually have arrangements exactly like that on a pixel level. They use filters for each pixel, doubling up on green. With something like this you might be able to combine the filter and the lens.
Your explanation of 'thousands of frequencies' is somewhere between misleading and incorrect. Electromagnetic radiation is a continuous frequency. Our eyes' 'sensors' are not sensitive to exact wavelengths of course, they are sensitive to a range. Some more sensitive to red, falling off into orange, into yellow, into green (as the frequency of light goes up). We are most sensitive to colors in the green spectrum, least sensitive to blue.
Do you know why the sky is blue? It is because of the spacing of ozone particles. It absorbs and reflects higher and lower wavelengths _more_ but red and green light still make it through, as well as UV radiation.
I think the difference is that a modern camera filters in wide ranges.
So blue is maybe 400-500nm, green 500-600nm and red 550-650mn.
But these new lenses only give sharp images in much narrower bands. If it has blue at 448-449nm, green 540-541nm and red 580-581nm, most of the spectrum will be lost.
It _is_ possible to do trichromatic color photography with sets of single-color filters. In fact, the earliest color photography was done this way. Technicolor films were shot in a camera that recorded three monochromatic strips simultaneously. (it is true that the filters were generally not strictly a single color frequency, but a narrow band)
The difference is that they were using film which was sensitive over the entire visible spectrum with color filters that allowed a broad range of wavelengths that are all perceived as the same color. If you had a smartphone camera filtered with a 1 nm bandpass filter for a particular wavelength, you're going to get so little light that it will be like taking pictures in the dark.
The filter approach is still used in most cameras (Bayer filters) but a vary narrow wavelength bandpass would not be appropriate for a consumer camera.
I don't mean the images displayed on a panel; I mean the light from the panel if it were used to illuminate something else. Because you have only three narrow wavelengths of light, you lose 99% of the color information contained in the illuminated object's absorption spectrum.
Actual LED lamps work around this issue by using phosphors to broaden the spectrum.
This quality of light is measured by the Color Rendering Index; the phenomenon of color differences due to narrowband light sources is known as metamerism.
The images displayed on a panel do not suffer this issue, because our eyes can detect only 3 "dimensions" of color; hence 3 narrowband illuminants suffice. (And in fact narrowband is necessary for a broad color gamut.) It is only when reflection/absorption comes into play that metamerism matters.
You could get some image with single wavelength red, green, and blue sensors, and it might be pretty interesting looking, but it wouldn't see much like our eyes do.
That would treat monochromatic yellow light differently from yellow light made up of a combination of red and green, instead of treating them the same like the human eye does. The yellow of an actual banana would distort differently from the yellow coming from a picture of banana displayed on an LCD.
