Early color computers typically had a limit of X colors used simultaneously from a palette of Y, a classic example being the Commodore 64 which could do 320x200 monochrome or 160x200 four colors, chosen from a palette of sixteen.
The limitation on the number of colors used simultaneously is a straightforward matter of memory bandwidth: it just wasn't possible (within the budget of a home computer) to pump more bits to the video chip per frame.
What's the reason for the limited palette size? Intuitively it would seem straightforward to e.g. have a palette of 65536 colors; it would just be a matter of having a few 16-bit registers in the video chip, easy enough even given the technology of the day. The resolution of the digital to analog conversion circuitry would need to be improved, but that doesn't seem like it should cost very much.
What am I missing?