fun fact: airplane mode is meant to prevent your phone attempting to connect with cellphone towers as its flying by, not to protect the connection between the cockpit and the engines.
Second fun fact: on android you can control which modules are disabled when airplane mode is enabed, though this is usually not exposed to the user.
Edit: while what I said seems to be true, radio transmitters, such as those in mobile phones, may interfere with some instruments, with GPS being most affected. However, if I understand correctly, these interferences are minor to none and I'm guessing issues start to arise when more devices are transmitting signals.
from what I understand, the issue is moreso that it can slow down or conflict with communication on the ground. Your phone won't be able to use the cell tower for long, as it is only close enough for a short time. if I understand correctly, another concern is a phone sending messages to a cell tower out of range conflicting with transmissions related to another cell tower.
Another issue is that this could lead to reduced battery drain, as sending messages to far away cell towers takes more energy.
Some areas allow aircraft to be equipped with low power cell towers (aka picocells), which both provides cell service to the passages and prevents interference with cell towers on the ground.
note that both the US and EU are mostly hands off: airline operators may choose to allow WiFi and Bluetooth, if they can certify their craft, with the EU allowing picocells to be equipped on aircraft.
Hope you understand what I'm saying, but I can try to answer some questions.
Note that bigger PIDs like laptops or tablets can also be a hazard.
Also both the EU and US give aircraft operators control over requiring device radios to be deactivated (with the exception of cell service in the US, as mandated by the FCC), as long as they show the aircraft can operate safely.