There seems to be an assumption here that empathy leads to morality. Sometimes, at least, empathy leads to being jerked around by the stupid goals of others instead of pursuing your own stupid goals, and in this case it's not all that likely to lead to something fitting any plausible definition of "moral behavior". Chogyam Trungpa called this "idiot compassion".

Thus it's important to distinguish caring about humanity as a whole from caring about individual humans. I read some of the links in the OP and did not see this distinction mentioned.