This post doesn't cover why someone would want to do this. If this is to reduce file size, using JPEG (or more modern AVIF or JPEG XL) directly will likely produce better looking images at smaller sizes. However, for lossless image compression, like PNG or GIF, reducing colors might be worth doing.

True-colour images use 24bit per pixel, which means that each pixel has three channels of 8bit, one for red, one for green and one for blue. The possible colours that can be displayed are 256³ = 16.777.216, wow… do we need all these colours in each image? The short answer is no.

Try telling that to a woman.