I'd be for this.
If I'm on call, guess what, I dont go to a movie! Shock horror! I take responsibility for myself and make sure that I'm actually in a position to do something about the emergency, should it arise. If I'm in a movie theater, what can I do about it? Borrow the managers laptop (Excuse me sir, this is a software EMERGENCY! People cant work here!). No, I make sure that if a call comes in, I'm close to my own laptop so I can do something about it.
A lot of people who are on call for emergencies seem to want to have their cake and eat it - go do fun things that put you far away from being any help but still have their cellphone available so at least they can be contacted. What good does it do? Even if I received a call and ran out, guess what, its distracting to other people.
Sadly a lot of people seem incapable of common sense and courtesy. If they were, then we wouldnt be having this discussion. And having someone strongarm someone who answered his phone out the theater is about as disruptive as the call in the first place, although I suppose long term that would mean such behaviour would decrease.
If there is an emergency with your child, they can do what they did in the old days - phone 911. What am I going to do for my child if I'm half an hour away, at minimum, and know nothing about first aid? if I hire a babysitter, I expect him or her to do what is right for the child, and that may include phoning the police, fire department, health services or me where appropriate. Phoning daddy is not always the answer - like as not an ambulance could respond quicker and give actual useful help instead of "it will be okay sweetie".
Yes I'd want to know, but my parents and their parents were okay with not knowing every aspect of their child's lives for 5 minutes. I think I can do that too.