Holding yourself in high esteem, even seeing yourself as completely flawless, always right, does not keep you from identifying with the plights of others. One has little impact on the other. Are all egotists, narcissists completely self-centered to the point where they don't care for others?
We have countless examples of people who have huge egos, but care deeply for their fellow people. They may think they are the best, but some even have more empathy as a result. Think of hollywood? Have you ever seen a bigger group of self-centered, self-important narcisists? At the same time, many of them, even as a result, feel that their status gives them the opportunity and responsibility to do good in the world.
Donald Trump has the biggest ego of any President I know, and he has zero empathy. If he had any empathy, he never would have made any of the sexist and racist comments he made during his campaign run. His ego is his main engine, and it overrides his conscience(if he has one) and reason(if he has any).