I need them for a step in a 2D shadow generation algorithm (which is on the CPU). I can do that step without min blending, but that step is currently by far the largest bottleneck in the algorithm, and with min blending the algorithm I'm using will handle hundreds of lights at high framerates, because it's largely independent of light numbers, where the algorithm used in "let there be light" depends on the number of lights on the screen. Also, it's on the GPU and practically doesn't use up anything on the CPU at all, which is good since most 2D games are very simple graphically and the performance bottlenecks are usually in CPU algorithms.
I will probably also need it for blending together signed distance fields sometime in the future. A signed distance field is just an image where every pixel of the image contains the distance to the closest obstacle. These are very expensive to create, but you can pre-calculate the large ones for static objects in your world and then only compute small ones for your dynamic objects and blend them together using min blending, too.
