Well... the existence of brain damage, in and of itself, is not evidence for this, I agree.

That is, if I lived in a world where (for example) brain damage existed but cognitive impairment didn't follow from it, in much the same sense that skeletal damage does not result in cognitive impairment in the actual world, the mere existence of brain damage would not tell us much that's relevant to the soul hypothesis one way or the other. (And, relatedly, in the real world I don't think the existence of skeletal damage is good evidence for or against the soul hypothesis.)

But I would also say that the facts that normal cognitive function reliably occurs in the presence of normal brain function and fails to occur in the absence of normal brain function, and that brain damage reliably predicts variations in cognitive function, and that there's no evidence that variations in the soul predict variations in cognitive function, constitute good evidence that souls are not causal to cognitive function.

If I've understood you correctly (which is by no means guaranteed) we disagree here.