Why 7? Our eyes have 4 different cells, so any system with more than 4 colors will lead to a system where we just have redundant colors that the eye can't tell apart
The possible colours form a sort of semi-circle known as a chromaticity diagram (https://en.wikipedia.org/wiki/Chromaticity). If you pick 3 points in the diagram then the triangle they form won't cover the entire shape. In fact since it has curved sides no finite amount of colours will allow you to fully cover the perimeter. But having more colours lets you more completely approach the perimeter.
That's one solution. Seven wide points on the CIE would cover it pretty well. Another is to have fewer points and dedicate extra channels to specular reflections, extra-spectral colors: https://en.m.wikipedia.org/wiki/Spectral_color#Extra-spectra... and imaginary, impossible and chimerical colors: en.m.wikipedia.org/wiki/Impossible_color and 'matrix' them with the color channels.
The challenges however for any new color system are formable and it would require new developments in technology before being practical.
The human eye is quite remarkable, it adapts dynamically to the situation in both its luminance and chrominance channels and has an effective dynamic luminance range of around 10^6 : 1.
To give you a sense of how truly adaptable the eye is here's an example: the now defunct Kodachrome - which was once the gold standard in film emulsions and in some limited ways still is - only had a luminance dynamic range of between about 250 and 500 : 1 (depending on how you measure it, 250 being more the norm), and its chromaticity was pretty limited especially in reproducing violet (violet being the least objectionable tradeoff) and yet it was capable of producing some quite wonderful photographs (and I've still many thousands of slides to prove the fact).
Now if you compare Kodachrome with what the eye is actually capable of then there's essentially no comparison, Kodachrome falls so far short you'd wonder why we'd bother using it at all. The fact is the eye adapts to that limited situation and does a remarkable job of fooling you into believing that the Kodachrome image is the 'true and real thing'.
This example also illustrates the very real difficulties in getting to the bottom of color theory. Keep in mind the issues here: real light consists of an almost continuous electromagnetic
spectrum, the eye resolves this by matrixing RGB primaries to produce an 'imaginary' spectrum and it also has to deal with extra-spectral colors such as magenta, and there are other issues as well.
As I hinted I'm reticent about entering a heavy debate about this subject here as I can only do so superficially - just one word out of place and it'll be mistaken as wrong and it'd only derail the debate.
Look, it's a huge subject: (a) our existing color technologies - video/television, printing and color film - are already very sophisticated and are full engineering professions in their own right - and as we're discussing all have quite severe limitations in their ability to faithfully reproduce the luminance channel let alone the chrominance one, and (b) the theory of color vision is not only complex and quite difficult to understand - and now it's become even more complex.
I will however finish with an idea I've had for years that could overcome many of the limitations of the tricolor (or any multicolor system). It's completely theoretical as the tech still doesn't exist. The idea would work like wideband superhetrodyne radio receiver. A UV laser as the local oscillator would beat with incoming light in a mixer to produce an IF (intermediate frequencies). The more manageable IF would be bandwidth compressed and eventually reconverted up-band to visible light so the viewer is actually seeing a spectrum of visible light. Simply, a TV camera of such system would capture say light at 555nm and that's what the viewer would eventually see - and not some mixture of RGB primaries. Picking coordinates on the CIE would be a thing of the past.
Now, I know the objections will be many and all sorts of issues both technical and theoretical arise but there's little point in debating them here.
I've raised this for one reason. The whole problem we have with color reproduction starts with the fact that we cannot reproduce the eye's CIE with true accuracy and using any number of CIE coordinates will never completely solve the problem.
Eventually, we need to find a better way. Finding a way to accurately record the incoming wavelength of light in recorded images would also provide us with many other scientific and engineering advantages.
