According to Wikipedia, the project originally had American writer J.M. deMatteis associated with it. While deMatteis might have done passably well in depicting the metaphysical history of the DC Universe, I doubt he'd have shown much facility with the other three functions. For instance, Gaiman doesn't just meditate on the metaphysical appeal of magic for the many characters depicted, but also the psychology of those attracted to "The Art." The cosmological strictures of science also contribute to the whole, particularly in Book 4, which depicts the entropy-death of the universe, complete with an "indigo shift" to replace the "red shift" with which the universe supposedly began. And almost certainly the American deMatteis certainly would not have been able to seed the BOOKS OF MAGIC narrative with its many trenchant observations on the differences between the world of American-made superheroes and the "universe" of the Comic-Book "British Invasion."
For instance, of the four DC heroes who oversee the narrative of MAGIC, two (Doctor Occult, Mister E) are American characters created by American authors, one (the Phantom Stranger) was created by an American author but had indeterminate cultural origins, and the last, John Constantine, was created by one of the leading scions of the British invasion.
Constantine offers a British perspective on the wild and woolly world of American superheroes:
I prefer to live in a country that's small, and old, and where no one would ever have the NERVE to wear a cape in public, whether they could leap tall buildings in a single bound or not.
And yet, for all that, BOOKS OF MAGIC also offers Gaiman the chance to create yet another British-born character who has the potential to be a "super-magus." Teenaged Tim Hunter, according to the four magical masters, is destined to become either a great good or a great evil. They appear to the bemused young man, offering to initiate him to the world of magic. The boy makes the choice to listen to them-- a decision fraught with later consequences-- and for the length of the mini-series, each of the occult teachers shows him some aspect of DC's magical universe.
The Stranger shows Tim the distant past of the universe, and gives him the first inklings of the price of magic.
Constantine, always the "cutting-edge" type, escorts the teen into the contemporary society of magicians, with some assistance from Zatanna.
Doctor Occult, a creation of Siegel and Shuster who predates Superman, takes Tim through the domain of faerie (a very British domain, despite the appearanc of the Russian horror Baba Yaga).
And Mister E, the most obscure character (who has only made ten appearances in a DC horror title), accompanies the boy to the very end of the DC universe, which combines aspects of H.G. Wells' TIME MACHINE and Gaiman's own "Sandman-subcosmos."
A single blog-post can't suss out the many ways in which Gaiman approaches the multivalent topic of magic, in concert with four of the most "painterly" artists of the period. But I will note in closing that Gaiman is consistent throughout the narrative in seeing magic as not just superstition or madness, but as the fundamental image of human desire, Or as Aleister Crowley said:
“Magic is the Science and Art of causing Change, on a material as well as a spiritual level, to occur in conformity with Will by altered states of consciousness.
A given reader may care nothing about the actual practice of ritual magic. However, Gaiman and his collaborators have eminently shown that even if magic had no reality in the world, in the literary world it remains a potent means of "altering states of consciousness."