They're all reasonable answers, but the whole thing seems a bit more 'justifying how D&D does it' than 'simulating how Appendix N does it'.
D&D was very bad at a key theme of fantasy fiction: the notion that wizardry involves an empirical investigation of the world.
Jack Vance, Clark Ashton Smith, and a lot of the older writers such as Dunsany, Machen, Blackwood, etc. portrayed magic as an Isaac-Newton sort of alchemical proto-science. In the Dying Earth, a wizard who rediscovers mathematics becomes game-breakingly powerful. If you wanted to model that in DCC, you would make the wizard a cleric, and you would make him the servant of the god of dispassionate mathematical reasoning.
Jack Vance, The Dying Earth wrote:
In this fashion did Turjan enter his apprenticeship to Pandelume. Day and far into the opalescent Embelyon night he worked under Pandelume's unseen tutelage. He learned the secret of renewed youth, many spells of the ancients, and a strange abstract lore that Pandelume termed "Mathematics."
"Within this instrument," said Pandelume, "resides the Universe. Passive in itself and not of sorcery, it elucidates every problem, each phase of existence, all the secrets of time and space. Your spells and runes are built upon its power and codified according to a great underlying mosaic of magic. The design of this mosaic we cannot surmise; our knowledge is didactic, empirical, arbitrary. Phandaal glimpsed the pattern and so was able to formulate many of the spells which bear his name. I have endeavored through the ages to break the clouded glass, but so far my research has failed. He who discovers the pattern will know all of sorcery and be a man powerful beyond comprehension."
So Turjan applied himself to the study and learned many of the simpler routines.
"I find herein a wonderful beauty," he told Pandelume. "This is no science, this is art, where equations fall away to elements like resolving chords, and where always prevails a symmetry either explicit or multiplex, but always of a crystalline serenity."
Arneson showed no interest in these themes; he wanted a game with no theoretical premises, just external improvisations. Gygax was similarly resistant to the idea that magic could EVER make any kind of sense. (Gygax seemed to follow de Camp's example in this regard, except that Gygax, unlike de Camp, was willing to imagine miraculous healing as a divine, but never an arcane, event.)
So if the wizard is a Rotwang or a Frankenstein or a budding fascist megalomaniac - then the wizard-as-Faustian-powermonger trope fits.
But if a wizard is genuinely interested in truth and knowledge rather than a frothy-mouthed megalomaniac bent on dominating a kingdom of slaves, the Faustian-powermonger trope does not fit.
now, in the last fleeting moments, humanity festers rich as rotten fruit. Rather than master and overpower our world, our highest aim is to cheat it through sorcery…. I am dissatisfied with the mindless accomplishments of the magicians, who have all their lore by rote."
In Vance's formulation, the quest for knowledge was the sole ennobling factor, whereas the dull stupidity of rote repetition and the foulness of human nature were both evils.
Since Blikdak is a demon .. ."
"Consider him!" spoke Kerlin. "His lineaments, his apparatus. He is nothing else but anthropoid, and such is his origin, together with all the demons, frits and winged glowing-eyed creatures that infest latter-day Earth. Blikdak, like the others, is from the mind of man. The sweaty condensation, the stench and vileness, the cloacal humors, the brutal delights, the rapes and sodomies, the scatophilac whims, the manifold tittering lubricities that have drained through humanity formed a vast tumor; so Blikdak assumed his being, so now this is he. You have seen
how he molds his being, so he performs his enjoyments.