Not totally relevant, but don't totally ignore interference from various sources, once had a compass problem on a 707, turned out it was a tape recorder - you know, the sort that were about the size of a portable typewriter and used reel to reel tape ( ask your dad ) - that had been loaded into the stowage above the seats - between two very large lines with the note : Do not load any electrical equipment here ! The permanent magnet in the loudspeaker was effecting some remote compass sensing stuff at that point.
Holding the phone near the ILS / VOR needles isn't the problem, hold the phone near the equipment that DRIVES those needles. Could be somewhere near where the phone is being used, as in my 707 case.
Murphy is always with us, but I agree, in small, VFR aircraft - no problem, just don't rest the phone on the glareshield, near the little compass suspended from the top of the windscreen !