I would think the color spaces of most displays have that, don’t they?

The bevel of a black iPhone is darker than its screen, even when powered off. Similarly, switched off CRT displays aren’t truly black.

Oh, I was just listing the constraints. I'm not directly aware of a color space where value 0 is not no light. It would however mean that even if linear, doubling a value relative to 0 wouldn't necessarily double the amount of light.

Most video color spaces have black at a non-zero code value.

The most common 8-bit YUV format (e.g. in MPEG-2) uses a 16-235 range for valid luma values, so black is at 16 and white is at 235.

The reason for leaving this “headroom” and “footroom” had to do both with digitizing analog signals and avoiding clipping during processing.