<I guess a few km long power cord would be inconvenient.

why is this a problem?
you can always have a high speed train with a nuclear reactor on it down on earth while having a powercord connected from the train to the plane
its an old design
also you can have a super powerful laser weapon on it, and the plane can have a radius of like 200km maybe, maybe even more

posting my todays invention: ICBMblock (can have more stealth design