I think the main problem is that we can more or less agree on a few types of things value wise, but really value discussions are pretty charged conversations that often won't end with a conclusive agreement, even if people keep their emotions in check. I think part of the reason is that, at some level, there isn't much to be done about dissent in values.
I can imagine an argument for, say, your example of what we should do about the homeless, but really I think no matter what we decide on there will, at some level, be a reason for some to be dissatisfied with the change. Also, I'm not really sure how this would be related to emotional intelligence. I think of emotional intelligence as knowing how to handle your own and other people's emotional aspects. I would argue that, depending on one's values, emotional intelligence could hurt or help a value-based discussion.