Too random
Would you like this new stat to be important or necessary?
If it is merely important, than having it being random is not a bad thing. Some characters will have more of it than others, which will create diversity; and those who absolutely want it will have an obvious way to gain it: get a large unit with strong weapons rating and set it to murderous.
If it is necessary, however, then I understand why you would want to make it more predictable, however please do think of the priests, infiltrators and other assorted characters when you design it. They are important too, and sending everyone to the warrior class will not in itself lead to more wars.
