AP article:

Study: Distracted driving laws don't prevent crashes

A new insurance industry study has found that state laws banning the use of handheld devices to make calls or send text messages while driving have not resulted in fewer vehicle crashes.
[...]

The Highway Loss Data Institute, an affiliate of the Insurance Institute for Highway Safety, said its findings "don't match what we already know about the risk of phoning and texting while driving" and said it is gathering data to "figure out this mismatch."

In my observation, one of the reasons why the laws have not shown a resulting change in number of accidents is that a lot of people are simply ignoring them. Okay, handsfree devices are more distracting than not being on the phone at all, but I still see an awful lot of people chatting away on their phones, same as always.