Here is a video from TED-Ed that explains why. TLDR: phones looking for a signal broadcast on high power, but planes move so fast that you can end up right next to a cell tower so the high power signal can interfere with other phones trying to communicate.

https://youtu.be/iKYHf22qVdM

I disagree with how he phrases a few things, but I think it's mostly accurate.

Most flights I've been on had outlets and/or USB for charging, I've been leaving airplane mode off for every flight for years now

Come to think of it, I'm pretty sure battery drain is about normal anyways when I don't plug it in, the radio must eventually switch to a lower power lower search frequency at some point. Either that or the tower searching drains your battery thing is about as overblown as the leaving GPS on thing

I turn on airplane mode whenever I am already connected to wifi

I thought another reason was to avoid blasting everyone* you pass with your phone's maximum power signal while trying to reconnect.

Edit: the problem being interference, not any health effects. I read that the effectively one-way signals from the sky worked somewhat like a jammer.