Two points on interference.
I've travelled with my cellphone in the trunk of a large car, at least as far from the car radio as you can be from the cockpit of a single aisle airliner. I can still hear significant interference on the radio as the phone searches for a signal - and I don't want that to occur at the moment ATC tell the pilot "immediate hard left for collision avoidance" or something similar.
Secondly as was mentioned above not all of the items that could be influenced are in the cockpit, there are looms of wiring and instrumentation throughout the plane.
Aviation has developed into such a safe method of transport by overengineering safety to a very high degree - this is another example of that.