Might as well have a Fox, Hound, Bird, Frog, etc. type.
Fox, and hound fall under mammal, Frog falls under amphibian, and bird is a whole class of animals its self. Dragon would be like the animal kingdom (or whatever) Insect, Bird, Mammal, Reptile, and Amphibian. They do have Bug. So I guess because they can and it's awesome.
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In hindsight, it probably would have been better for GF to have made it a "Mystic" type. That is sensible. As it is, it's too late to change, and unlikely they'll make a new type. Besides, Dragon is fine as it is.
Light type wouldn't make sense because all of its aspects are already covered.
Light source - Fire, Electric Holy - Fighting
Fitting a Light type in would just conflict with the types already established. A light bulb Pokemon should be Electric not 'Light', it's the same thing. A devout holy warrior should be Fighting not 'Light' etc.
I haven't seen anywhere that Fighting in Japan is defined as Holy. Can someone point me to a source on this? I just checked Bulbapedia and while it mentions that Dark is known as Evil in Japan, it retains that Fighting is just Fighting in Japan.
If this is the case then the Light element makes sense as a holy element or "good" element as opposed to Dark.