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Blue noise is broadly useful in imaging, you can use it for high quality dithering, or for perceptually smoother sampling in raytracers for example.

Here you can see the same rendering using white noise (true randomness) or blue noise, with the same number of samples:

https://www.shadertoy.com/view/3sfBWs / https://i.imgur.com/uDybnPm.png

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Not only in imaging. More generally, blue noise is often used with all kind of Monte Carlo simulations, since the more evenly spaced sampling can speed up convergence. Raytracing can be seen as one such MC simulation

In path tracing blue noise does not increase convergence, but does reduce the perceptual error.

The upper bound of the approximation error of random Monte Carlo methods decreases with O(1/sqrt(N)), whereas the error for quasirandom Monte Carlo methods (omitting some details) decreases with O(1/N) (where N is the number of samples) [0]. I don't think path tracing is an exception here.

I would even argue the opposite: For the same variance I would expect the error to be more perceptible for (blue noise) quasirandom MC, because it can lead to regular patterns in the noise.

[0]: https://en.m.wikipedia.org/wiki/Quasi-Monte_Carlo_method

Thank you. Now I understand the use case.

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