There may be lots of problems with emergencies all over the world, but dialing the actual number isn’t one of them.

well, there’s a couple benefits i can see to a quick-dial: in an emergency situation time is of the essence and you want as little hassle as possible in reaching emergency services. maybe for some reason you can’t dial well, or at all–maybe you’re panicking and a shortcut button gives you a less entropic way of calling emergency services.