Filament won’t mix in the nozzle, it is laminar flow. That’s why the multi-color filaments still print multi-color instead of becoming a mix.

Also, as someone else pointed out, color printers do not mix ink, they put tiny dots on the page - like pixels on a monitor. In fact, basically everything you look at today with color is using tiny dots of color and dithering to make it look like a different color. So, it sounds more like your problem here is that FDM printing does not have the resolution needed to make the dithering effect indistinguishable at the distance you would like. Which may be fair, but it is more likely that someone invent a way to significantly increase the resolution of FDM prints than it is that they would find a way to mix any color you want from CMYK filament “on the fly”.