The age is important because of the other things going on in life that are foundations of the rest of their lives. A 16 or 17 year old, still in High School should have a lot of things on their mind: doing well in school, applying to college or deciding on a future, enjoying themselves, etc. The reason that we make the cut off at 18 is because that's what the government says is the point where someone can make a decision was to their own life, whether they want to work in EMS, McDonald's, or go on to study medicine at John Hopkins.
I'm 20 years old, and when I work as a medic some people still get nervous at how young I am, and I have an associates and am close to a Bachelors. How do you feel about having someone work on you that can't possibly have a High School diploma?
As for all the comment's about how it helps a person mature, I've seen a number of 16 and 17 year olds that choose to neglect school for the Ambulance or Fire Dept. To the extent of skipping class to go hang out at the Ambulance Bay. In a lot of cases this field attracts people for a little while, where they will devote a ton of time to becoming an EMT and making it to every last volunteer call, and then burn out. To have that happen to someone that is a senior in High School...