I totally agree, I strongly believe (= I have not done any trial or calculation, which is not scientific) the thickness is one of first order parameter.
You can find here a work (sorry in French) made by a gentleman call Claude Boutet. He concludes, what intiutively looks logical, that the thiner the material is the better it is. The only proble that a infitively thin material does not exist. And from what I can see mathematical approach usually assume an infinitively fine material.
I'm sure, the thinner the better. My pinholes are laser cut into a 0.04 mm foil, which means the hole/thickness ratio is about 10:1. With this ratio, thickness has little influence. As the material gets thicker, light rays bouncing off the hole inner walls will cause optical disturbances and thickness (and the smoothness of the inner walls) become a factor. But this is not an issue if the hole diameter increases by the same factor, because the ration is important. As far as I know, there is little research on this topic.