Particular, it's hard to deal with anisotropy, and naive approaches to fix this hurt either break the operation as a dither with uniform dot sizes, or struggle to avoid becoming regular at angles.
I agree with the claim, though, that you lose quite a lot by having the dither pattern stuck to surfaces. There is a charm to it for sure, but a high quality screen space dither would be cool. And so I experimented with some ideas and came up with one. Forgive the jank, I'm learning as I go.
https://www.shadertoy.com/view/WfBGzK
Note that this is using a random dither versus a patterned one, which I think hurts the aesthetics a lot, but I am certain this is incidental to the concept. I think there are probably much smarter techniques, and I have an idea for a large rewrite already, but those are details, just take this as a proof of concept.