Perhaps all the operators you just completely lost your respect for were swamped with calls from other people dialing in with other cell phones reporting your accident and/or other people reporting their minor collisions (Clue! quantumet, 911
is an emergency
number, as you say. If nobody's life is in danger and the situation is pretty stable, you should be calling the police, not 911. If you don't have numbers in the car (shame on you!) you should be dialing the operator.)
At least they were hopefully doing more than you were, sitting on your butt with your cell phone. (And incidentally, if you're being raped, a handgun is going to be a lot more helpful than a cell phone.) Even under ideal situations, emergency staff can't work miracles. They can't instantly beam to the site or make your trouble disappear. And the ideal situation is seldom actual.
In short, in the end you've got to fend for yourself. Emergency response folks are mostly hard working. If they have shortages, it's probably not their fault. Don't blame them; do something about it. And above all, don't abuse emergency services. Save it for the folks that really need it.
And if you are in trouble and can't get through in an emergency, keep your head and call someone you can get through to. Remember the adage, "Call for police. Call for an ambulance. Call for pizza. See who comes first."