It's too early to really question the effectiveness of texting-while-driving bans, but certainly not too early for the insurance industry to speculate. A recent study by the Insurance Institute for Highway Safety apparently demonstrates that states with texting bans do not see a reduction in crashes. In three states crashes actually increased. An Institute spokesman claims this may be a result of drivers moving their phones down and out of view to avoid being spotted by police, thereby taking their eyes off the road longer.
Keep in mind, these laws have only been in effect for a few years, so there is little data to study, and it is more difficult to distinguish other factors and trends.