I like the concept of disconnecting paladins and clerics from gods. Discipline, codes, and faith give power in the real world, even without direct intervention of deities.
To bring up wizards and why they can't heal, I think a strict adherence to either oaths, or some code, and faith in themselves or said codes, give them the mojo to do so. Wizards may be mightily intelligent and very disciplined, yadda yadda and all... but it takes a certain mindset and mental state, and maybe even some sacrifice to gain "divine" magic. That sacrifice may block them off from arcane magics in favor of the divine. The world in MnM is sentient, so who knows in lore where their magic comes from.