The Mythbusters episode on this was pretty well done. Of course most phones have no effect on most electronics. But in order for anyone (like the FAA or the airlines) to certify them as safe, they'd have to test every single mobile device against every single piece of aviation gear. There are hundreds, if not thousands of different pieces of gear, and the prospect of performing actual tests of every possible combination is just wildly impractical. And... there's a constant stream of new devices on the market every day. It would be all but impossible to keep up. It's simpler to just ban them all.
Fly by wire planes also present a problematic EMI situation.
>> There are hundreds, if not thousands of different pieces of gear, and the prospect of performing actual tests of every possible combination is just wildly impractical. <<
I beg to differ. I have the distinct impression that potential interference is power-dependent and frequency-dependent, not really device-dependant. That is, the type of device and its modulation scheme would not seem to be important. I should think the problem basically ought to be trivial for an RF or avionics engineer who specializes in interference : Spend enough on shielding and you’re home free.
(I’m not an engineer, don’t even play one of TV. So if any of FR’s multiple RF engineers want to shoot down my “theory,” please don’t hesitate.)