In the era of analogue video, when you needed to connect a local video source (STB, VCR, game console, DVD player, etc.), the most ubiquitous way to do so, next to using an RF modulator, would be to use a composite video connection. But it only carried a video signal - for audio you needed a second RCA cable. And as the audio is often in stereo, it became common to see triple RCA cables with colour-coded white, red and yellow plugs on both ends.
Now the question is - why not just carry the audio signal, modulated in the same manner as in a broadcast channel, within the baseband video cable? It should not significantly affect the quality of either video (as the audio subcarrier is outside the video bandwidth) or audio (as the audio carrier frequency of, depending on region, 4.5-6.5 MHz - and its bandwidth - are high enough to encode all audible frequencies). Stereo could also be carried the usual broadcast way (MTS, A2 or NICAM).
I don't know what is the practical bandwidth for a typical composite video cable, but in PAL regions, the baseband signal already carries the 4.43 MHz chroma carrier - around the same frequency that NTSC (and PAL-M/N) audio is on (4.5 MHz), so I guess that suffices as a proof of feasibility at least in NTSC regions.
Analogue video devices used to commonly include an RF modulator anyway - so all the logic necessary for modulating that FM (or AM in France) audio signal was usually already there - so it shouldn't significantly affect the price of the device.
Such arrangement would allow to connect a baseband video source with a single cable - which seems like a pretty good convenience and selling point - connecting a bunch of identical plugs can be error-prone, especially with the less technology-savvy customers.
In addition, composite video cables can get much thinner, longer, more robust and cheaper than e.g. the afore-mentioned SCART cables - I can see many people willing to accept the sacrifice in quality (compared to S-Video or RGB offered by SCART - and many people wouldn't even see the difference) for the greater flexibility in cable arrangement gained this way.
So... why was it never done that way?