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Where do I start. Let's separate colour gamut and number of different colours.
The gamut is set first by the system primary colours. The current primaries for PAL/NTSC differ slightly from the original NTSC primaries. The HD primaries (Rec709) differ slightly again giving a slightly larger gamut than PAL/NTSC. This theoretical gamut is then restricted further by the cameras and displays. CRTs have, if anything, got worse over time though the introduction of rare earth phosphors helped a bit. More with brightness than gamut. In practice it's not too important. The TV camera and CRT makers have done a pretty good job. Gamut limitations only affect the most saturated colours. The various flat panel technologies are all over the place. None match the CRT phosphors but the best are pretty good.
Number of different colours is more difficult to quantify. I've seen CIE diagrams with arrows showing the least colour change the eye can see in different areas. This can only be established by subjective tests and varies with actual colour.
An 8 bit per component digital system can meet the eye's requirements here. The problem is that certain sorts of pictures can make the quantisation very obvious. The engineering test waveform "shallow ramps" is designed to expose this. Even a 10 bit per component system can be exposed this way. 32 bits are irrelevant. No TV system has ever used a total of 32 bits.
Now let's look at analogue. Although this allows an infinite number of colours the practical limit is set by signal to noise ratio. 48dB SNR is roughly equivalent to 8 bits. You would be very lucky to get that all the way from camera to receiver in an all analogue chain. Chroma SNR is worse than luma so even a superb analogue chain is probably working at the equivalent of 20 to 22 bits overall. Ever since the 1970s there have been digital islands within the analogue system. More recently the only analogue parts have been the camera head, transmitter and receiver. Eveything else has been digital. Often 8 bits, more recently 10 bits.
In a digital system you can trade quantising errors with noise. If you add a small amount of random noise to a shallow ramps test waveform the step effects will disappear while the noise itself will be impreceptible.
None of this addresses what happens during compression, more properly called data rate reduction. This is more complex.
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