At a lower-level, function composition is a form of stack discipline, where ordering is important, but placement less so.
In any case, I'm sure you can write a compiler that translates from X to Y, for some X and for some Y, using only Tic-Tac-Toe as your language, with readings from the back of Lucky Charms as the totality of your knowledge base. My point was that to really know compilers, you need to know a bit more than that.
What it is is a gateway drug to serious computing, including compiler construction.
However, let me just come back to your point that stack discipline is necessary for control structures and non-local transfer of control.
Well, that depends on the execution model of the machine, and I would say explicit stacks are a performance hack, made to model the mathematical concepts of closure and application.
Sorry, I had to remove my wordy examples explaining "Scope and Extent", and how they can be represented with environment pointers, and heap allocated activation records.
TODO: Point yet again to the "3 Implementations of Scheme" paper, Scheme being the cleanest Algol variant this side of modern computing.
Then I found this:
I was reacting to this statement you made, "Few chapters of a Lisp book will spare you volumes of traditional compiler construction techniques".
S. P. Jones' text was more interesting. I also like "Modern Compiler Design" (http://www.cs.vu.nl/~dick/MCD.html), which covers imperative/oop programs as well as logical and functional paradigms.