Airplane mode is largely pseudoscience/an abundance of caution/solving a different problem than a safety one. There's approximately zero chance of a phone interfering with avionics, especially modern ones, with their very low transmission power.
Supposedly the real reason has always been that mobile network operators don't like the interference high-altitude phones can cause: They're in view of potentially many base stations, some of which might be using the same frequency (which is possible since far-away regular-altitude phones are below the radio horizon and therefore not an issue).
Some evidence for this theory: The "mobile phone ban" is an FCC regulation, not an FAA one, and many (non-US) airlines have been offering on-board microcells for decades without any issues.