Why can "a set of [plural noun]" be written as "a [singular noun] set" but not "a [plural noun] set"?

Question

"A set of tools" can alternatively be written as "a tool set" (or toolset), but "a tools set" sounds very unnatural.
The same can be said of a number of other examples: "a book pile" vs "a books pile", "a paper stack" vs "a papers stack", etc.

Why is this the case? Why is "a tool set" correct but not "a tools set"?
What is the name of this kind of grammatical structure?

JeffUK · Accepted Answer

It's simply because "tool set" is compound noun, and you may have multiple tools but you only have one tool set.  In exactly the same way that toothbrush is correct and teethbrush isn't.

Why can "a set of [plural noun]" be written as "a [singular noun] set" but not "a [plural noun] set"?

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