Maybe your point is that emotional empathy feels morally significant and when we act on it, we can feel that we fulfilled our moral obligations.

This actually has a name. It's called moral licensing.

Yes, emotional empathy does not optimize effective altruism, or your moral idea of good. But this is true of lots of emotions, desires and behaviors, including morally significant ones. You're singling out emotional empathy, but what makes it special?

I agree with you that nothing makes them special. But you seem to view this as a reductio ad absurdum. Doing the same for all other emotions which might bias us or get in the way of doing what’s moral would not lead to a balanced lifestyle, to say the least.

But we could just as easily bite that bullet. Why should we expect optimizing purely for morality to lead to a balanced lifestyle? Why wouldn’t the 80/20 rule apply to moral concerns? Under this view, one would do best to amputate most parts of one’s mind that made them human, and add parts to become a morality maximizer.

Obviously this would cause serious problems in reality, and may not actually be the best way to maximize morality even if it was possible. This is just a sort of spherical cow in a vacuum level concept.