(I'm making a dumb reference to ICE engines here, but actual batteries where air participates in the reaction are a promising area of research that could greatly improve battery energy density.)
Wouldn't that just be a fuel cell?
Obviously a drawback is that existing airfields' or airports' runways would have to be retrofitted, but if the fuel and maintenance savings were enough, it might make sense.
[1] used on aircraft carriers: https://en.wikipedia.org/wiki/Aircraft_catapult
I'm sure Boeing or Airbus could create prototype liners and only have a few airports with catapults built into the airstrips. You could save a considerable amount of energy if it's designed correctly. Plus airplane tires have to be replaced very frequently. It could reduce takeoff wear as well.
Probably not the craziest idea ever.
While the "refueling drones" are circling overhead waiting to charge up a transport jet, may as well use them as five mile high wifi access points for internet, and divebomb amazon deliveries. I mean they're up there, may as well make use of them when they aren't charging jets.
Think of the FAA madness WRT flight plans and mandatory minimum "fuel" and alternatives/diverts. The paperwork alone for aerial refueling on plain old passenger service is likely to get weird.
Meanwhile if solar panels get cheap and durable enough, or safe enough in a crash to plow thru, charge the drones off panels laying around the airfield.
In theory you could have 100% solar powered high speed aircraft transportation using this weird system.
Note that you can cross the ocean if you have a dense enough fleet of charger drones. By dense "enough" I have no idea what to say here.
You need enough battery power to get "up there" and to cruise between drone hookups (which might only be a couple seconds if the drone comes along with you, or if you have dual charging ports I guess that means zero...)
Note that every airframe full of people requiring 2 or 3 smaller airframes full of batteries will be an interesting capital cost to work around.
I don't think there's enough surface area on an airplane to gather significant solar power. And that doesn't help at night or in clouds.
A jet turbine generator can run at near-constant efficiency.