If they can predict which site you're on, they can also possibly detect an unsecured secure algorithm's state.
SSL or PGP had a similar "power starvation" attack: reducing the power to the power supply and watching power drainage allowed one to predict private keys.
The attack has been patched, then.
Summary is here [0], and paper is here [1].
[0]: https://www.theregister.com/2010/03/04/severe_openssl_vulner...
[1]: http://web.eecs.umich.edu/~valeria/research/publications/DAT...
iOS does a lot of thing during charging. Face recognition, backups, mail checks, software updates, another applications' background stuff.
It might as well interact with your home or car over BT (cars have wireless charging these days). There's a myriad of opportunities there.
* https://www.rammount.com/shop-all/phone-mounts/wireless-char...
Or just offer free wi-fi and watch people’s traffic.
And this ‘leak’ assumes a user has his phone on a charger while it is already full, there is no guarantee it works.
If that's correct then what's the actual real world problem here?