Eliminate banding in color gradients with dithering

When the desktop background is set to a gradient, especially one with colors that are clsoe to one another, considerable banding can be observed. This is not very visually pleasing.

While it's not possible to add more color range to an existing system, the effect can nonetheless be almost completely eliminated by introducing noise, aka dithering.

Below is a mockup that uses Gimp's Filter -> Noise -> Spread to spread pixels around randomly by up to 100px in the gradient direction only. 100 seems to be a good value. Any lower leaves visible banding, above will start to introduce visible noise

Before:

After:

This might be an easy way to eliminate the banding effect.

Thanks!