If you had an RGB (24 bits) image that is mostly very dark, would you say that somehow because the image doesn't use the full range of possible values, the image quality suffered? Would you say that changing the format/bit-depth would actually lead to a perceived increase in quality when looking at the image?

I don't understand why you said I was wrong in the other comment, but you give here an appropriate analogy which makes the effect obvious.

Because we only have 8 bits per channel, we all can see banding in (dynamically) compressed images. That's what increasing the depth improves.