Speed is the problem aswell as driving quality and failure to pay attention.
Good drivers drive "To the system of car control". Alot of problems are caused because people fail to knock the speed off before a hazard and because they are to keen to get their speed back up.
Although I do agree too many people think they are good drivers. You can be the best driver in the world but if you don't drive with the capability of the car, road conditions and your own limited ability in mind. Its only a matter of time before a near miss becomes a fatal accident.
Allowing yourself to slip into "Drive mode" where you go through three sets of lights on your way into work but don't remember any of it is one of the most dangerous things people can do. As out of all of the things your mind might pay attention to in that memory lapse (Traffic lights, other cars, radio) vehicle speed is often forgotten.
Speed certainly is a problem: the faster you're going, the shorter your reaction time and the longer it will take you to slow down. That's just basic physics.
The problem is that the road safety campaigns give an over-simplistic message that speeding is the only problem, whereas it isn't. Poor hazard awareness, inattentiveness, lack of consideration for the prevailing conditions and a host of other reasons contribute towards accidents, as well as excessive speed.
Unfortunately, until we stop focussing on the moronic "speed kills" slogans, and improve driver training and police enforcement of careless driving and driving without due care and attention, we won't see much of an improvement.
If you're a bad driver, driving 1mph under an arbitrary speed limit doesn't make you safer than a careful driver travelling at 1mph over it.