Empathy is indeed powerful. And, if people understood each other better, I do think it would mostly be used for good. Conflict is rarely a constructive outcome, so even the self-interested would probably try to use it to broker peace.

The problem is that empathy isn't evenly applied. We can more easily gather empathy for people who are like us than for others. Asking people to be more empathetic may very well exacerbate the lopsidedness rather than reducing it. That uneven distribution of empathy makes it very difficult to make good, impartial decisions when their interests are in conflict.