Clerics in B/X don’t get a spell at first level so they spend the first few adventures UNABLE to heal people. This gives them a chance to learn more roles, like throwing holy water, turning undead, backing up the fighters or defending the mages, and so on.
1974 D&D and the various incarnations of basic (Holmes, Moldvay, Mentzer, and the Rules Cyclopedia) do not give clerics a spell at first level. Strangely, some of the retro-clones (Labyrinth Lord, LotFP) do give first level clerics a spell. The clones that don’t are Swords & Wizardry Core, Swords & Wizardry WhiteBox, and Original Edition Characters for Labyrinth Lord. I believe the AD&D Player’s Handbook was the first place that first-level clerics are given a spell, though more knowledgeable people can correct me if I am wrong.
In any case, I much prefer the no spell at first level version of the cleric. It highlights the martial aspect of the character class, which I think is very important to the cleric as demon hunter and crusader rather than purveyor of cure light wounds.