This may be an over simplification, but aren't 3 physical dimensions the minimum number needed for space and matter to exist?
If you shave away one of those 3 dimensions from a material object, that object will be gone... it will cease to exist. It seems somewhat convenient that the universe managed to coalesce into a minimum number of physical dimensions before it was no longer able to create any more dimensions. So I'm thinking perhaps 3 isn't a minimum or maximum... maybe it's the only number of dimensions the universe was (physically) able to produce.