1. The FF1 white mage was clearly based on the D&D cleric; it had blunt weapons only (except for the Masamune, which to kids in the 80s not familiar with Japanese culture could be some mystical weapon), healing, more HP than the Black Mage (wizard) but less than the fighter, and the spells, apart from stuff like the HARM series which was supposed to replace the turn undead ability by doing damage to undead only, are frequently supposed to be ports of D&D spells. Apart from healing and resurrection, there was AFIR and AICE (resist fire, resist cold), PURE (neutralize poison), MUTE (silence 15' radius), and EXIT (word of recall). The black mage spells were similarly copies of the D&D magic-user spells; BANE was pretty clearly cloudkill, there are nonrenamed (albeit truncated to 4 letters for English release, because Japanese needs fewer characters for a word) copies of sleep, hold person/monster, haste, confusion, slow, and teleport. And, why do you think the three major elemental attacks were (and continue to be!) fire, cold, and lightning? There's even a bit of a nod to the old level structure with ICE coming one level above FIRE and LIT just as you got fireball and lightning bolt at 3rd level and ice storm at 4th. The D&D connection even explains some of the stranger design decisions; there were high-level stun and kill spells that didn't work on monsters over a certain number of HP alongside others that did, which makes no sense unless you read the spell descriptions for power word stun and power word kill.
Basically, lots of computer-nerdy people in the 80s thought D&D was the coolest thing ever and most early CRPGs on either side of the Pacific were attempts at being able to play it on the computer without running into copyright.
2. If you do a sort of class role analysis, the wizard is a pure DPS, the fighter is a pure tank, and the cleric is a hybrid tank/healer. (The MMORPG 'holy trinity' thus descends directly from the original three classes of brown-box D&D, which says something I'll let someone else figure out.) So there is, theoretically, a role for a 'hypercleric' pure healer, for completeness' sake if nothing else.
But I haven't seen a lot of them, and I've seen a lot of these OSR rebuilds--they love to remake the elf fighter/mage we all loved from 1e, but somehow the hypercleric never comes up. (The only example I've seen is Adventurer Conqueror King's priestess. I've heard there's a doctor class from an old Dragon Magazine that had bad combat but got raise dead at a lower level, but nobody seems to have followed up on that.) I suspect given the way tabletop RPG play is still centered around combat, a pure healer role isn't that much fun as it's purely reactive and you wouldn't have much to do most of the time. Also it may be insufficiently macho for the still-largely-adolescent-male gamebase--it's significant they had to call the healer role 'leader' in 4th edition.
3. Religion's always a tricky topic, but they seem to have stayed far away enough from that to avoid trouble since the 80s, and by the time they came back to it the culture had changed. But they have been removing pantheons like the Hindu (yup, 1e Deities and Demigods had stats for Krishna) that are still worshipped--it's notable the 3rd edition version of Deities and Demigods had the Greek, Norse, Egyptian, and Greyhawk pantheons...none of which have a lot of actual worshippers these days. (I don't know if Norse heathens lodged a complaint or not. I'm curious now.)
4. D&D has become its own Thing at this point, with its own archetypes that influence fantasy fiction. Lev Grossman's The Magicians even nods to this by having the wizards research the spells from the Players' Handbook! So even if the Cleric doesn't fit another archetype, I'd say it's its own, and has become such a central part of the game it's hard to remove. Kind of like the way you occasionally see people trying to get rid of the Wizard, but there's too many people who really want to play D&D so they can play a bookish academic with magical powers.