I agree with everything else you're saying but this point is spurious. Clerics don't exist in the real world. RW Priests aren't magic-users (not in any D&D sense anyway). That's like saying "When did you last see a Beholder in RL?!" to justify Beholders not being in your game. It makes no sense.
As for the general point re: armour, if you have some Cleric subclasses not having armour, that is going to need to be balanced somehow. Currently only one two classes in 4E who don't have armour by default - Wizard and Sorcerer. They also both have d6 HP, limited weapons, and better access to offensive spells, particularly ranged damage ones. It's also problematic because the main class' armour access is the base for the subclasses, so the Cleric would need to go having no armour as a base, and subclasses all adding it. This would be a bit of a nightmare.
That's why the suggestion of two separate classes is a lot better. Cleric, which we could leave alone, frankly - perhaps just add one "Generic" domain (name it however) which offered generic Cleric abilities roughly equal to the specialized ones. Then you have another class, probably called Invoker or Priest something like like that, and that has a base of zero armour, and better access to offensive spells like a Sorcerer/Wizard.