Half of Exalted doesn't make sense. By bolding your statement, you implied it was a rebuttal to my claim that the dragon kings actually suffered more for the War, to the point of their peaceful civilization's collapse. In any case, it makes sense in the context that A) the dragon kings were apparently created by gods and B) mortals, even mortals as mighty as the dragon kings, were incapable of truly harming them.
Humans were chosen to receive the shards for the same reason raksha died en masse trying to eat them during the First Age: they have something bizarre, special, and somewhat explosive in their souls. Additionally, most other races were either too close to beasts or too hierarchical. Humans were chosen for the same reasons they are in D&D: no tendency to law or chaos, no level adjustment, no attribute penalties, one free feat at first level.