Yes, it absolutely should be against the law. However, unless this statute was actually enforced, it would be essentially useless.
Several years ago, my state (NJ) made it a secondary MV offense to talk on a cell phone while driving, unless one uses a hands-free device. As a secondary offense, a driver could only be ticketed for this violation if the car was stopped for another reason (burned out lights, illegal turn, etc.)
A little over a year ago, talking on a cell phone while driving (without a hands-free device) became a primary offense. There was a fair amount of publicity that this would be strictly enforced, and a few local PDs actually did engage in a ticketing blitz for a few weeks.
However, at this point, this statute is largely ignored by drivers, with the effect that virtually every woman piloting a 3-ton SUV to the corner store is holding a cell phone and yakking while driving. And, this widespead violation of the statute is the result of essentially NO enforcement.
Banning texting while driving is an excellent idea. But, unless there is an actual effort to enforce it, I believe that the legislation would merely be a feel-good exercise in futility.