What is the relation between colour spaces and what is actually displayed on our screens? I am not entirely sure that this is the right stack exchange, but I couldn't find any other suitable one - please redirect me if necessary.
There exists mathematically defined colour spaces which help us represent colors with accuracy/efficiency in computers, and different color spaces will capture different ranges of the human visible colour gamut, and because our screens cannot represent colors as raw wavelengths we must use these spaces instead.(correct me if anything said there is wrong)
How do these relate to how our computer screens actually show colour? From what I understand, our screens only take in N-bit RGB signals for their LCDs, so why do we worry about having all these complex, computationally expensive colourimetric spaces, when we want to do colour processing or storage etc. For example, the sRGB space has a gamma encoding, to represent a different data range with the same amount of bits... but that gamma encoding (for a greater range of dark tones?) cannot actually be displayed on screen. And CIE xyY might be excellent for spectrum based rendering and accurately producing and grading colours - but I understand that we cannot actually see their results, only RGB approximations. Again correct me if any of the above is wrong! I say none of this with much authority, which is mainly why I have to ask this question :)
We are storing different, nuanced, &quot;perception correct&quot;, data in this 8-bit channel format - but is that extra nuance is  lost as soon as we send it off to our raw RGB 8-bit channel screens, and if so, doesn't that loss invalidate (to some extent) all our extra measures to produce ever more accurate and wider gamuts?
This question focusses on R8G8B8A8 displays, as I imagine HDR would have a different story.
Several reasons. Im listing them in random order

There are entire industries that do other things than display things on computer screens. If you were to print a booklet, make a package, movie projection or paint a car you would probably be wise to be able to mathematically model it for design, quality control and documentation purposes.

Not all screen suck and not all are good. Quite many screens out there can show wider color ranges than sRGB, or wider but still not entire sRGB. See sRGB is well suited for the designs it was designed for namely crt screens. LCD screens have had  hard time coming to sRGB gamut, but we are getting there. So many screens can not even do sRGB and many now exceed it.
The RGB color on each screen is different! Unless you have a screen that has been calibrated to sRGB odds are low that it shows sRGB (even if it does bet goes off in few weeks). Now for most people this is ok they arent aware how much off their screen is (i remember calibrating for first time o was quite shocked).
Anyway point is that you might be interested is describing the color so that you can do same color, not just same numeric value, on a different screen or display technology.

You might be doing color science and communicating measurements to others, or calculate how fast humans can separate the colors.

You might be developing a light simulator, i dunno like for movie special effects and or technical design and your interested in the light spectrums.

You might need to do distributions of colors visually


And so on...
As for gamna encoding your screen is not linear. If your screen were tuned linear it would be crappy indeed. And in anycase good screens have 10 to 12 bits of color to work with so gamma correcting is no problem.
As for spectral colors CIE is not dealing with spectrums... Not at all. All 3 component color is dealing with human perception. Spectrums are way different things, the thing you call orange on screen and what your physics book called wavelength are different things.