Speeding is not involved in the majority of fatal accidents.
1) Speeding is illegal. This is a law that is broken every day by millions. Obviously the law and the punishments aren't working as a deterrent, and the next steps usually involve control rather than deter.
2) Do you know how reaction time and braking time change for every 5mph faster you're going? It might not make you cause an accident, but it sure doesn't help trying to avoid an accident.
from http://www.motorists.org/speed-limits/faq
Q: Is the National Motorists Association a reliable source for this data?
A: I did the 30 seconds of work to go and Google this, go find your own stats if you don't like mine.
Almost all accidents are "speed related". Very few accidents happen with cars standing still.