NES uses 16 colors simultaneously on the screen. If you see at games like Final Fantasy, 4 grayscale colors are almost permanent on the screen; two for interfaces and several things, black and white).
There are almost 4 colors for the charas, 2 for backgrounds and I think 2 more for objects or enemies.
Indeed, the GPU of NES is 4bits, not 8bits, ahd that has a lot to say on processing power. SNES had about 7 or 8 graphic modes, and each with variations in dimensions and more. GPU have some data processing capacity which is reflected in the screen resolution and color depth (in computing the resolution is for example 800x600x32, because that is the size in bits graphic data display buffer).
Consoles were 8-bit referring to the CPU. Similarly, PCM chips (music synthesizers) allowed values 8bits equally manageable with 8-bits, for consistency with the CPU and probably to facilitate data handling.
Also, the sprites are 8x8. If you remember (?), Most things used textures sizes equal to powers of 2 because it is easier or faster for the processor to handle such data.
PD.- My english sucks...