Your instincts sound good here.
Yes, it might help in a few cases. The Associated Press Stylebook warns, for example, against referring to all black Americans as "Afro American" because many identify as "Afro Caribbean" or in other ways. That's an excellent point a sensitivity reader might raise.
But my sense--from talking with other authors and journalists--is that overall the readers are having a troubling chilling effect. I'm hearing stories of novelists getting slammed by them for stereotypical portrayals of minorities when the whole point of a book is to fault those stereotypes through satire or another device too subtle for sensitivity readers.
Writers are starting to avoid worthy and important topics because--in addition to all the other barriers they face to publication--they now know they risk running afoul of one-issue readers. If this keeps up, American literature will be the poorer for it.