You might also note that the increase from 2k video resolution to 4k increases the opportunity for dithering. Since 4k resolution is overkill for showing picture detail at ordinary viewing distance, you can trade some of that unneeded resolution for more colors. I looked up product literature for some 4k video cameras, and noticed that they capture images with 10 bit color and dither that down to 8 bit color in the recording.

Greg
VP180, M80s, M22s, QS8(4), CSW S305s, EP500, Pioneer VSX-90
M2i, M3(2), Pio vsx-1020