It's strange how when we hear that term, 'workplace' we think of the typical IT-type open-plan office with everyone crouched over computer screens. This sort of environment appears to breed discontent as people 'climb the corporate ladder.' Certainly emotional intelligence will help ease a lot of self-created pain here. But there are jobs were emotional intelligence is pretty well requisite.
For example, I spent many years in Aircraft Operations. Such people as air-traffic controllers don't 'spit the dummy' if something doesn't go smoothly. I'd say the same would apply to fire-fighters, ambulance drivers, theatre operating staff and a host of other occupations.
How can companies develop emotional intelligence in their staff? A whole new culture would need to evolve, starting firstly at the leadership level where as, say, in the little Kingdom of Bhutan in the Himalayas, 'Gross National Happiness,' is deemed more important than Gross National Product. In other words, the happiness of staff being involved in meaningful, enjoyable and rewarding work was regarded by all as more important than profit.
The companies' leaders would need to have the emotional intelligence to see this as a company mission, of course, and not just pay lip service to it. But I expect some organizations, the ones that allow great freedom for the employees to make decisions and implement them, whether deemed wrong by the hierarchy and no punishment dealt out if a project fails, such as many of the Silicon Valley enterprises - these leaders are already using a emotional intelligence.