Actually, I would say that a society ruled by "empathy" would quickly collapse, as the people in charge would be unable to make decisions based on an objective cost/benefit analysis, but instead would be paralyzed by emotional concerns. It's a common cliche that "you can't put a price on human life", but every modern society does, constantly, and if a society's leaders can't do this, the society will fail.
To use a highly oversimplified example: Let's assume that we can prevent 50% of automobile related deaths by imposing a regulation that increases the cost of a car by $1.00. Most people would say that would be worthwhile. To prevent 50% of the remaining deaths, we can increase the cost of a car by $100.00. To prevent 50% of the remaining deaths (this report was commissioned by Zeno, by the way), the cost increases by $1000.00. And so on. There is a point where someone must say, "Yeah, the harm done by increasing costs that much outweighs the value of the lives saved." An "empathic" person would be unable to draw that line, as he'd be unable to say "Some known percentage of people will die in accidents, people who COULD have been saved if we'd spent more money." This carries across many different fields and areas of human activity, from drug trials to engineering. There's a point where some level of risk must be deemed "acceptable". The more empathic someone is, the more difficult it will be for them to consciously allow a certain number of probable deaths or injuries.
Emotions are easy to manipulate. I show you (generic you, not you personally) a bunch of pictures, along with heart-wrenching stories, of Palestinean children killed by Israeli bombs. "How can we support such murderers?", you ask. Then I show you heart-wrenching stories of Israeli children killed by Palestinean bombs. "We have to protect these people!", you cry. If your decision is based on how much you CARE, you can't make a decision. You have to step back and evaluate which side, if either, is more useful to support for reasons totally irrelevant to how many children are getting killed. You have to reduce people to numbers and statistics -- or you can't decide, and meanwhile, even more people die while you waffle.
More abstractly, there will always be more problems than there are resources to solve them. Someone has to decide whose suffering to alleviate, and whose to ignore. People who are too empathic can't; at best, they'll make decisions based on whichever crisis is most heart-touching to them (usually determined by which one has the best propaganda), not on other considerations.
Most of our society, at all levels, can only function if we set aside our feelings and focus on facts. An umpire shouldn't make calls based on which team he wants to win, even if his motivation is sympathy for the feelings of the team that keeps losing all the time. A boss shouldn't fire or hire people based on who he likes more, but on job performance. We disdain those who show favoritism to friends and relatives, but it is psychologically normal to be more sympathetic to those closest to you. It is psychologically *abnormal* to make decisions without regard to your emotional connections to people -- but people in power are expected, even required by law, to do precisely that, to decide things without consulting their feelings.
Thus, it is inevitable that those with the least empathy will rise to positions of power, because those with the most can't do the job.
(I've run into a depressing number of people who are convinced this is not the way the world is; that if only we all CARED enough, there'd never be a need for hard decisions, because everyone would just do the right thing, all the time.)