I always though Clerical healing was kind of dumb when Wizards didn't heal also if it's all going to be based on "magic". Arcane energy can re-write history and change the cosmos yet you can't seal an axe cut with it?
I view certain types of magic to change reality so much that mere Wizards cannot do it. Clerics cannot do it either. The Cleric's Deity does it. Only the gods have this level of reality changing ability.
What do Wizard really do? Summon some creatures. Throw some fire around. Teleport. Go invisible. Wizards are, for the most part, charlatans when compared to the Gods. Illusion, opening up portals to areas of fire or lightning, moving energy or objects from one spot to another. They can be viewed mostly as transportation specialists, creating energy and effects where they do not currently occur.
These effects can be powerful, but they are not anywhere near the level of complexity and control of magic that healing a wound in real time should conceivably be. I think the reason Clerics have deities in the first place is because Gary envisioned healing to be something that mere mortals could not do, but Gary needed healing in his game system.
Granted, everything I wrote here is a rationalization of how I view magic and my view is based on 3.5 decades of playing D&D and similar games.
But, I do think there are some (mostly) "sacred cows" in D&D that do not need slaughtering either. Just because someone can think of an idea doesn't make it a good idea, nor does it mean that the game designers should seriously consider it.
I think self healing in 4E was extremely irrational from an in character perspective, but makes sense from a "keep the game flowing" out of character perspective. It's effectively taking one of the most powerful magics in the game system and handing it to everyone for free.