The blip where clerics gain 3 spell levels in 2 classes is an odd one (for reference: C5: 2/2, C6: 2/2/1/1, C7: 2/2/2/1/1), but it's also inherited from OD&D. And if you look at the spell lists in OD&D, the 3rd and 4th level spells are almost entirely passive, the only exception being sticks to snakes (animal growth and striking are new additions in B/X). So the net effect of gaining two new spell levels in a single class level isn't a power boost, it just means 6th level clerics gain the ability to remedy most maladies (curses, diseases, AND poisons) at one time. Being able to cast 5th level spells is the real jump in power.
Which relates to the power level of spells. BTW, if you want an example of spells that appear remarkably underpowered, look at create food. You can either raise the dead or slaying the living by pointing at them -- or create a day's worth of rations for 12 people. Yay! In general, healing is weak in old school D&D, and that includes AD&D as well. It's more about removing status effects, like poison or disease. And when combined with the cleric's weird progression, it's a mistake to compare the SPELL levels of cleric and magic-user spells. It's really about comparing the spells that can be cast by a cleric and a magic-user of the same class level, or even better at the same XP total. A cleric can cast 5th level spells at 7th level, or 50,000 XP. By contrast, a 7th level magic-user can cast 4th level spells, while a magic-user with 50,000 XP can cast only 3rd level spells. So finger of death, raise dead, quest, and commune are comparable to fireball, fly, haste, lightning bolt, charm monster, confusion, massmorph, polymorph others, polymorph self, wall of fire, and wall of ice. Which doesn't seem overpowered to me. The magic-user has far more offensive options, and the cleric is better in certain narrow areas.
The XP table for clerics is generous, even more so after name level (why do clerics advance more quickly than thieves?), but even so clerics are second rate at fighting and casting in combat (and that's being generous). Even with their rapid progression, they don't eclipse the fighter or the magic-user, and really only shine in the healbot support role, or by making fights against undead relatively easy, so they're not overpowered or spotlight stealers.