What, No Cleric?

Playing the Game without the Cleric Class
White Box offers the player a choice of three character classes, Fighting Men, Magic Users and Clerics. This intimately connects the game to a religious assumption, however one defines the Cleric's faith. Healing wounds, curing disease and raising the dead are the purview of the Cleric and divine magic. Magic Users seem more elemental with their fire balls and lightning bolts. The Cleric and his/her associated religion are not to everyone's taste, however and many competing game systems (Tunnels & Trolls, The Fantasy Trip) do not include the Cleric class. Clerics are not usually found in Sword & Sorcery fiction except as evil magic using priests. The quasi-Christian "holy warrior" template seemingly used for White Box's Cleric finds no precedent except in crusader-era history (and some Hammer horror films?).
So what happens if we take the Cleric out of our game milieu as a player class? I think it changes the tone of the campaign. Without player Clerics the gods seem more remote and somehow less real which removes some of the "magic" from the game. White Box and all its subsequent Editions relies heavily on players managing the resource of hit points. Healing hit point damage gives a character resilience and allows for recovery from misjudgments or plain bad luck. There are other sources of magical healing, but relying on potions and healing surges changes the nature of the game, perhaps making it more to the liking of some, but less for others. Healing spells can be made available to Magic Users which is how Tunnels & Trolls, The Fantasy Trip and some other games without the Cleric class addresses this need. A non-religion based dedicated healer class (herbalist, alchemist, etc.) is another option.
Given the role religion has played throughout human history the Cleric class seems a natural fit in gaming to me, even though the cleric/priest is rarely a central character (except as an occasional protagonist) in the fantastic literature from which Fantasy RPGs draw inspiration. Therefore there is some understandable creative tension regarding the class. The originators of White Box, and therefore of the hobby, obviously used fantasy religion as a central theme in their campaigns. Gary Gygax not only includes the Cleric in his campaign, but in Supplement I: Greyhawk adds the Paladin subclass of Fighters. Paladins are in many ways just another version of the "holy warrior" ideal which serves the basis of the Cleric class. Dave Arneson gives us The Temple of the Frog in Supplement II: Blackmoor which being the first published adventure from an original campaign centers on a religious monastic (Keepers of the Frogs) temple complex and evil high priest/Cleric (Stephen the Rock).
In my experience the game works perfectly well without the Cleric. I have refereed many a table at which there was no Cleric PC (undead are more powerful in the absence of a Cleric). I have played various systems without the Cleric class and they all work. Removing the Cleric class from White Box (and later Editions) does alter the game, however. As creator of your milieu, perhaps the stories you wish to support and inspire do not involve Clerics or religious warriors. Part of the creative process involves shaping the milieu by deciding what character classes (and races) will be available to play. I see this as "casting" as for a movie or play. Who are likely to be the central figures in the cooperative story that develops during play? You get to decide!