As something of a tangent, one "traditional" fantasy setting (read: elves, dwarves, orcs, etc...) that did Dwarf Wizards right was Earthdawn. I always liked the way it removed itself from the Tolkienesque influence while managing to keep the dwarves dwarf-like and the elves elf-like. If anyone is looking for inspiration as to how to "justify" dwarven wizards (or many other "against type" portrayals of demi humans in general) they could do far worse than look at Earthdawn.
As you pointed out, Tolkien actually gave spells to the dwarves. I am not sure why D&D established that they weren't wizards, but it did and it has its own mythology just like Earthdawn can have its own. The question therefore, ultimately, is if you think dwarves can be wizards in D&D. Unless I have a player who really wants to play one, I wouldn't change the mythology. And as to this thread's question, it's "against type" because that mythology is still cherished. Too many dwarven wizards would ruin it.
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