Tbh i have never really liked the idea of clerics wearing armor. I always found that more of a Templar/Paladin/Knight thing, which we kinda already have minus the magic.
For the record, that IS what a Cleric is, in D&D. A Knight Templar/Hospitaller, at least according to the old AD&D 2e players handbook I still have. Crusaders of their God(s) defending their flock by going out and adventuring and smiting evil. The later creation of Paladins (They were added in 1e, I THINK?) muddied the water, which is why they're confusing in AD&D 2e.
Clerics to me have always been robed monks and priests, who maybe at best are armed with a war mace or such, but never been full on "warriors".
That's a priest, not a 'cleric' by modern gamer lexicon (At least in the West, across The Pond). Which ironically, D&D never made as a type of 'NPC'. They always made them the armour wearing knights. Or they there were just people who worshipped but had no Divine casting ability.
As for the restriction, i think it is a bit of both. It is something that to my understanding (I have not played any of the older editions) have always been part of the game, but i kinda like the idea that if you wanna use magic, you can not use iron equipment, both as a nerf but also as a narrative thing (i recon it takes inspiration from cold iron).
Something i would prefer over having an "Cleric class" specifically would be something that could be more universally applied to "religious fantasy archetypes". Like perhaps "Acolyte", which could be applied to such positions such as priests and clergymen, cultists (be the thing they worship or not, you can be a cultist without being evil), druids or shamans etc. It might not start magical but i found fun the idea fun to play.
The issue to making 'clerics' I have is the way that Animism is described, it's very witch or herbalist druid, rather than a form of actual holy worship. But that's NOT a problem. I'm fine with healers being more woodsy, and having actual Priests with Magic Power, especially high up in a local religious establishment having two Magic power sets, depending on their object of worship.