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Ok so here's the actual reason:
It has nothing to do with the plane, if phones had even a slight chance of making a plane crash they would not allow phones onboard.
It has to do with cell towers, when a phone can't connect it keeps raising the antenna power to increase its range and try to get to a tower this is not a problem on foot as when it does find a tower it is far enough that it works as intended. Now when you are flying a 600mph and you blast a cell tower at maximun power you degrade the signal for everyone else that cellphone tower is connected to.
Adding: in some areas (EU and possibly India, unsure) the aircraft can be equipped with a low power cell tower called a picocell to both supply cell service to those on board and to prevent this issue.
The EU and US also don't require planes to be unaffected by WiFi or Bluetooth signals, but allow operators with aircraft assessed to be unaffected to allow passengers to use the aforementioned radios.
I've also seen some studies suggesting phones may pose slight interferences with the planes GPS system, but it didn't have much weight.
That actually makes all the sense as to why a phone dies 10x quicker when it has no service
There's a slight potential for all of those phones at max power to have an effect on the airplane's avionics. It's very unlikely, but they use an abundance of caution due to the potentially fatal outcome. What you described is true, but it's not the only reason.
Also 100 people with phones that trying to get a connection at max signal strength can interfere with plane communication.