One study over a short period may not tell us a whole lot anyway, but
My own experience over the last ten years owning both cars and phones is that yes, using a hand held phone will driving isn't a safe thing to do - did it once or twice and stopped. I have a hands-free kit for the last 6 or so years, and I think it really depends on the call - happy to chat to someone (mainly my wife) low involvement conversation - how was your day, how where the kids, do I need to pick up something from the shop, etc. And happy to take work calls where I'm a passive listener - but anything where I need to think and engage is lethal - tried it once, I'm told that in the middle of a passage of technical advice I just unconsciously started talking about road conditions and other cars - bad, but better than the alternative where I suspect I would have crashed - didn't try that again.
So I guess to me the problem here is that the behavior we want (drivers to focus on driving) and the action taken (banning hand-held mobiles) are loosely aligned, but the action may well not be having the effect we want.
Of course, one other possible reason - lots of drivers didn't use handheld mobiles when driving without the band being in place - I wonder if this group overlaps heavily with the group who would automatically obey the ban?