EMS isn't just about driving the ambulance...
Emergency Medical Techs and Paramedics are the frontline in emergent care.
Part of what is happening is that you must know what is going on the "frontlines" while you're sitting in front of a computer and talking on the phone. You have to be the eternally calm person who can pretty much handle anything. Think about it like this: If someone told you the building was going to blow up and you only had a Hockey ticket (ala MacGyver) to diffuse the bomb...could you handle it?
Moreover, there is a question of morals and ethics that needs to be handled. People may be yelling at you on the phone that so-and-so is DNR and the EMT's are trying to revive them and you have to try to calm the person down and somehow communicate with your personnel what the situation is.
Also, you will have to be able to direct people in what to do BEFORE your EMT's arrive. It would be pretty easy to just say, "Remain calm and the ambulance will be there any minute", but sometimes things need to be done because the ambulance might not be moving fast enough for the situation. Are you the kind of person who can handle that kind of pressure?
The next step in becoming a dispatcher is the realization that you are "technically" a manager. You're making sure people get to the places they are supposed to go without much trouble. This is a great position from which you can get promoted into a supervisory role and increase your pay. Also, it would be smart to WANT to work in the field as well. Being versatile makes you more desirable as a potential employee because you can do it all.
Sometimes we forget that there are two sides to EMS. The side you fall on is very important and helps to save lives. If you like a challenge and want to be put to the test then working as a dispatcher is the perfect job for you. Not everyone can handle the heat, but if you can stay "in the kitchen" then you've got a good career ahead of you.