At the time when dithering was commonly used to achieve the illusion of more available colors, i.e. the 80s and the first half of the 90s.
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It’s really only helpful for formats that will be directly read by hardware (the video chip) and where the “compression” ratio (I would prefer the term quantization) needs to be fixed. For file compression, which was quite mature but CPU- and memory-intensive at the time, the dithering only makes it more difficult to compress further.
Compressed textures on modern GPUs actually use similar compression: a color palette followed by indexes into the palette. But that’s done per 4x4 pixel block.
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I’m thinking of file compression formats like Zip, LHA and ARJ, which would work particularly well if the image was not dithered and used run-length encoding (e.g. the PIC format of the Atari ST). The PNG format still uses the deflate algorithm which is essentially identical to the compression used by PKZip in 1991.