Fascinating! Does that mean you could improve performance further with Floyd–Steinberg dithering? (I.e. instead of rotating randomly, you track accumulated quantization error and add that amount instead.)
Floyd-Steinberg is one sort of quasi-random algorithm, but there are others. People often use quasi-random rather than true randomness when they want to avoid sample points bunching together. They tend to be more evenly distributed. That can get more important in higher-dimension space where it's easy to completely miss sampling large volumes because a truly random point set has too many degrees of freedom.
Though these methods have their problems and blind-spots, too, and are often outdone by random sampling with even slightly higher sample count, while preserving all the simplicity and (statistical) guarantees you get from randomness.
But images have regular adjacent pixels to work with. Don't think the algo can be straight applied to irregularly placed points in manydimensional space.