Li Shenron
Legend
First of all I see no reason why all the spells you wrote in the first list could not indeed belong to the Wiz/Sor list as well. For example I never understood why Animate Object is for clerics and not for wizards? Find Traps? Air Walk? Silence?
I think the reason behind most of them is just D&D tradition: someone gave these spells to clerics once, and no one complained loud enough about the fact
About healing magic, the subject is more complicated.
1) To one side, it is still a matter of D&D tradition, and I bet that other RPGs don't associate healing magic with religious figures at all. That means you have all the right to break the tradition and make what you want in your setting.
2) To the other side, there's roles (strategically speaking). In basic D&D divine casters cover the healing role, and if you give other classes the same abilities, you are just shifting the role from one class to another or - more appropriately - "spreading" the role over more classes. Just ask yourself if this suits your game, because it may not necessarily be a good thing for the wizard
who might be "morally required" to focus on healing the others.
3) Finally, the balance issue is really non-existent in this case IMHO. At least because arcane casters won't know these spells "for free" like divine casters do, and as such a wizard is perhaps going to learn a couple of healing spells at the expense of a couple of utility/defensive/offensive spells less. Frankly it doesn't change the balance AT ALL, unless you are perhaps using the D&D rules to play a sort of arena game instead of a RPG. Would be far worse if you moved wiz/sor spells to the cleric list.
I think the reason behind most of them is just D&D tradition: someone gave these spells to clerics once, and no one complained loud enough about the fact

About healing magic, the subject is more complicated.
1) To one side, it is still a matter of D&D tradition, and I bet that other RPGs don't associate healing magic with religious figures at all. That means you have all the right to break the tradition and make what you want in your setting.
2) To the other side, there's roles (strategically speaking). In basic D&D divine casters cover the healing role, and if you give other classes the same abilities, you are just shifting the role from one class to another or - more appropriately - "spreading" the role over more classes. Just ask yourself if this suits your game, because it may not necessarily be a good thing for the wizard

3) Finally, the balance issue is really non-existent in this case IMHO. At least because arcane casters won't know these spells "for free" like divine casters do, and as such a wizard is perhaps going to learn a couple of healing spells at the expense of a couple of utility/defensive/offensive spells less. Frankly it doesn't change the balance AT ALL, unless you are perhaps using the D&D rules to play a sort of arena game instead of a RPG. Would be far worse if you moved wiz/sor spells to the cleric list.