Cleric magic and wizard magic are often considered to be inherently different, with cleric magic flowing from gods and wizard magic flowing from something else. Third Edition formalized this by creating the categories “divine” and “arcane” for spells. Fourth Edition added the concept of power sources explicitly, including several other categories like “primal” for druids and “psionic” for mind powers. The differentiation was present before in the “spheres” of Second Edition and spell lists of First Edition too, but the metaphysics was ambiguous. The OD&D text hints in several ways that maybe the two kinds of magic are not actually so different.
What if there was no difference between cleric and wizard magic, and clerics were just church-sanctioned sorcerers? There would be no question about whether church-wizards were conversing directly with gods or causing miracles. In a way, it would be like governments controlling access to weapons, with the added wrinkle of “purity” systems that come with religion. The restricted spell list would make sense, because those would be the spells known and taught by church authorities. Perhaps they are only taught by certain sects, and are subject to schisms within the church proper. Such conflict could be grist for an entire campaign. Clerics less oriented to the holy warrior archetype could use the magic-user class mechanically, but with the cleric spell list.
This probably demands some sort of colors of magic system as well, to prevent the blandness of a magic-user without principles just accumulating and casting all the spells. A while back I wrote this thing about magical affinity, which is one way of doing it if you want to penalize stepping outside the archetype without totally forbidding it. Alternatively, you could also just handwave the restriction and assume that black wizards can’t cast white magic and vice versa (or maybe white wizards can be tempted to the dark side, but the transition is irreversible or very difficult to reverse).