I'm fine with limiting the serious healing spells to the Cleric sphere. Again, a little bias; because another game I like, World Tree, has everyone knowing a small amount of magic of everyday/household use. For that reason, I'm fine with any character knowing healing spells that don't mend bone, repair nerves, raise the dead, or stop internal bleeding.
I did not have any of the pregens I made for a convention game develop any spells outside their professional spheres. This topic has given me reason to think on that.