One reason to use Blue noise in graphics / games / images is anytime you need a random number per pixel for, say, some Monte Carlo process, that will have a visible effect on the image and result in visible noise in the output. Using blue noise, the output will be visibly less “noisy” looking than when using white noise, due to blue noise having no low frequencies.

Blue noise is best for situations where you only have the budget for 1 or 2 samples per pixel. The very low sample counts is where it performs considerably better than white noise. If you integrate with many samples, tens or hundreds or more, then the advantage of blue noise over other “colors” diminishes.

The author of this post has some examples in other articles on his blog, for example using blue noise vs white noise for ray traced soft shadows. https://blog.demofox.org/2020/05/16/using-blue-noise-for-ray...