Back when I worked for a datacenter (involved hauling equipment from site to site at times), they had a similar policy.
They did checkups by calling you when they know you are in transit...you answer, the first time is being told to stay home the next day....without pay. Second time you're fired. No exceptions.
Basically it just made you turn off the ringer and be a good driver. I didn't care the reason, since it made perfect sense to me. I despise using the phone while driving......you can kill someone by not paying attention on the road far more easily than someone die from you not answering the phone.
In event of ER staff, they still use pagers in this time and age...I know, I have family members who are ER staff....and yes, they still use pagers. it goes off, they go in. That simple...no gab time involved.