Linear interpolation in the HCL space is not equivalent to linear interpolation in a linear colorspace. For example in a linear colorspace if the interpolation goes from saturated blue to saturated yellow, then the the interpolation goes through gray, while in the HCL space the interpolation goes through more or less saturated colors.

The possible colors produced by a display remain a cube in a linear colorspace, which is a convex object, so all gradients remain available.