We truly live in the age of instant gratification.
Just because there was a ban on using hand-held cellphones while driving doesn't mean people stopped using them while driving.
It would be interesting to compare with anti drinking and driving laws during their first 6 months and the levels of enforcement of each.
The study explains why they choose to review those time periods. The primary reason is to control, as much as possible, for other possible factors such as changes in technology, speed limit/road changes, weather changes, etc. By placing the time periods as closely together as possible they were able to minimize other variables.
There are other studies referenced, I cited the most recent study.
Nonetheless, you stated it perfectly - "just because there was a ban. . . doesn't mean people stopped using them while driving." Which is, after all, both the point of my post and the conclusion of the study. Ergo, the law did not and does not do what it is intended to.