You can pick any N pigments and they won't be able to produce a full range of colors when combined, and it's always an issue in every domain. Colors physically don't cancel out colorfulness (i.e. not-grayscale-ness), so mix cyan, magenta, yellow, whatever, you end up with a very dark color with some color to it, which is brown.
In particular, this is why you can't get HDR by just turning up the brightness: the primaries are different. The bright red isnt just brighter, it's "redder than red", and the same for the other primaries. Imagine an HSV color picker, but you can turn S up to 200%
Which, I suppose, is basically what you said, but I've spent the last couple days diving far further into color science than my little battery monitor really needs, so the details were on my mind.
You probably already know this, but there is such a thing as "the reddest red." A single wavelength of light is fully chromatic. As you mention, most color spaces use a "less red red," because it's easier to produce.
Some color spaces do use impossible primaries in order to capture more area but, as the name suggests, they are unphysical.
https://en.wikipedia.org/wiki/ProPhoto_RGB_color_space
Supersaturated colors do somewhat exist, but these rely on human visual oddities.
https://en.m.wikipedia.org/wiki/Adobe_RGB_color_space
or maybe better to say it was an error of convenience.
Adobe engineers had plans to harmonize their RGB with SMPTE 240M but something didn't quite jibe, and Adobe RGB was compromised to merely extend green of sRGB to cover cyan ink for offset printing.
As was previously alluded to, RGB creates a triangle of gamut coverage in the numerical space of the CIE 1931 and 1976 projections of the spectrum locus.
This trait of straight lines is mathematically convenient for calculating colors from primaries, and CRT display devices follow the RGB model closely. But commercial printing color coverage doesn't fit a triangular RGB projection very well: commercial CMY devices present a lumpier gamut with an area of significant extension of cyan outside of sRGB.
—Keep in mind color names are colloquial and a color wheel is an satisfying artistic contrivance that dates to earliest science of color, but in context of CIE diagrams, CMY are modeled as –R –G —B. (minus).
One one hand, sRGB was an excellent compromise of good coding efficiency, which means effective use of scarce bits in 24 bit color, needed to control quantization noise a.k.a. "posterization" / "banding" by not wasting codes on colors that rarely occur, while on the other hand completely covering the industry standard Macbeth Color Checker 24, the design of which was strongly informed by color film response.
The sRGB edge of cyan lives precisely at Color Checker 24 cyan and all the other patches live inside sRGB.
But electronic devices have surpassed film and are now far more common.
Ultimately DCI P3 would become a better fit with Apple's Display P3 variant (sort of sRGB v2) offering sRGB luminance response and a very slightly weaker cyan than Adobe RGB, but a much more generally useful extension to red, which for coding real world colors is more desirable than the furthest edge of a cyan which only occurs in inks and dyes, e.g. hitting a cyan spot color in commercial printing is not a compelling use case for most of us.
