Touchcreens are a problem
It is almost impossible to operate a touchscreen device without staring at it. Not just glancing at it but actually watching to make sure you touch that sheet of glass in the exact, visually indicated spot and nowhere else. By comparison, one could easily unlock and redial a button-gen phone without ever actually looking at the device at all.
For similar reasons, it is also impossible to drive a motor vehicle safely without actually watching the road. In most cases, haptic cues from other cars, pedestrians or even signage only indicate that things have already gone horribly wrong.
The upshot then is that it is impossible to drive a car and operate a touchscreen at the same. When someone is actively dialing a call or texting from behind the wheel, they aren't actually driving, theyre just sitting in the driver's seat of a moving car while they do something else. They stay on the road only by context switching back to driving frequently enough that the unattended car doesn't have time to wander off the road entirely.
There's a psychological challenge here. Driving does not require a great deal of mental effort, just constant attention so we, as humans, get bored and start looking for ways to use that time more "productively". In the absence of a passenger to talk to, the mobile is the natural outlet for that restlessness. As anyone who has made a reservation while driving can attest, this can work very well indeed.
Legislation seems essential but is fundamentally flawed to the point that it increases risk in some circumstances. While it discourages some users, others will just try to hide their activity. This, in turn, greatly increases context switching overhead and negatively impacts both tasks.
This problem will get much worse as most new drivers were texting for several years before they ever got behind the wheel. For those people, telling them not to text is kind of like telling those of us of an previous generation not to talk or not to listen to the radio. Good advice when driving but preceived as unreasonable in practice.
IMO, the real solution comes back to self-driving cars and better transit. The real value of handsfree legislation is not so much to punish texting and driving as to reinforce the point that it is not reasonable to text and drive and to help us progress towards reasonable solutions where someone can communicate while en route without endangering lives.
(note: I refer to texting throughout but, aside from the observation about young drivers, this applies to any manipulation of a touchsreen device).