The problem is not your everyday takeoff and landing. The problem arises when the weather deteriorates to near zero visibility and the crew is relying on instrumentation to find that strip of pavement, at 130 knots.
Instrument approaches rely on a narrowing volume of radio signals, the closer one is to the runway. The tighter the signal, therefore, the greater the deviation should something go wrong. Think of threading a string through a funnel, if you touch the edges, you lose. Now do it on a trampoline while someone else jumps on it. I assume we can all agree that wildly porpoising a 200k lb jet, 400 from the ground, chasing a signal, is not a good idea.
Vehicles on the ground are prevented from encroaching on the approach signal area, when aircraft are shooting approaches in reduced visibility conditions, to prevent them for interrupting the signal. In the cockpit you can see your signals fluctuate if someone does cross that threshold. It happens.
When visibility is good, it is a non event but when you can't see jack, having your guidance just start dancing around, gives one moments of pause.
The phones do interfere in some manner. TO what degree, I can't say. I have forgotten to turn my phone off before takeoff and get the annoying beep in the headset when we descend into an area with coverage, so something is going on.
The reason they ask you to turn it off is because they can't tell you its okay, because they haven't tested it. They can't say, well turn it off if it's cloudy or if the bases are below 300'. Some departures and arrivals require precise navigation, even in good weather, for traffic flow reasons. Missing a fix on departure or arrival could cause traffic alerts or aircraft deviations.
All rules exist for the worst possible scenario. Not the milk run. But how do you explain that to the traveling masses? You should be more concerned with the fact those little dixie cup oxygen masks they instruct you to put on in the event of a decompression, won't actually supply you with oxygen when the shit hits the fan at altitude. It's a partial pressure thing.
That's just between you and me...
Edit: At the end of the day, it is the law. If the crew is having a bad day and has a stick up their ass, they can make your day a lot worse. You need to ask yourself, does ignoring the rule, no matter how inane you think it is, really make a body cavity search worth checking the latest XKCD update?