Cell phones and other electronic devices can interfere with the pilot's comms and other crucial avionics, as well as cell towers on the ground, if the plane is low enough. Due to these issues, the FCC forbids using cell phones on planes, while the FAA allows airlines to choose when they may be used, once the plane is out of range of the ground cell towers.Source
The fact is, though, many people just don't put their phones on airplane mode. You can forbid it all you want, but without enforcing it (not feasible - too many ways to get around it), it doesn't do much.
Enter the Faraday cage.
Faraday shields are, in short, metallic surfaces that prevent the transfer of electromagnetic waves from one side to the other; Faraday cages are ones with holes in them, blocking waves of specific wavelengths while allowing all others through. You've surely seen Faraday cages before; they're in the doors of all microwaves.
This seems to be an easy (perhaps somewhat expensive) solution. Just put one up on every airplane, maybe with a wire going from one side to the other to allow the on-board Wi-Fi to still work. But it would block all outside communication, regardless of if you've got airplane mode turned on or not. If the cage is routed around/inside the sides of the planes and across the door between the cockpit and the cabin, the pilot would have no problem communicating with the outside world.
I feel like I'm overlooking something obvious, but I can't put my finger on it. Is there a hole (so to speak) in this theory?