This is a really great blog post by Daniel Goleman on the dangers of an empathy deficit. My experience is very similar with Daniel’s perspective: given the rapid pace of change and disruption today, most leaders are totally overwhelmed and often isolated. The trap of go-go-go actions and decisions often trumps space for a leader to reflect or dive into honest, exploratory conversations with customers, partners, and customers. In other words, the focus on task often trumps insights into how people truly feel, which is the basis of healthy, nurturing, long term relationships. 
As organizations grow, and people stop knowing or interacting regularly with each other, the need for leaders to cultivate greater empathetic skills actually grows faster than the rate of complexity and can be quite difficult to realize until it’s too late. 
Empathy is valuable for leaders across a range of the leadership spectrum:
1) Do my people connect and care with our vision? How would I recognize it, and how might we celebrate it and build upon it such that it grows in impact?
2) Do we have clearly defined organizational brand and values? In what ways do share, design and celebrate them them into all aspects of our work? How do keep them relevant?
3) How does my personal style, and the way I lead the executive team, demonstrate our desired leadership style? How would I know if I inadvertently limiting personal leadership in others?
The bridge to increased empathy is to be clear on how you are perceiving the world, starting with your emotions and the emotions of others, intentionally cultivating a broad spectrum of information, purposefully integrating it, and then being very curious to see the (mis) match between words and deeds of yourself, your executive team, and the larger members of the organization.  This is not something easily done independently, but can be an incredibly powerful and satisfying part of an executive coaching engagement.