Useful addition but not a rule or answer to the actual question. It's basically a systematic reiteration of the question. The rules that produce this pattern are AFAIK still to a large extend unknown.

Except for the latter two, that is: "Material" and "Purpose". These are actually quite easy to explain. What is called "purpose" here refers to simply compound heads that would form 1 word in other Germanic languages spelling, so obviously it comes closest to the noun. And "material" is a genitive that doesn't tolerate adjectives between it and its noun. "The wooden big table" is ungrammatical in a way pretty similar to "The table I saw of wood" is.