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.
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.
(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?