Given the power requirements of flight — they're fuel efficient per passenger-kilometre, but they have a lot of passengers and go a long distance — planes are the only place[0] where I think "overproduction by nearby solar farms" just isn't going to be a thing.
OPEC paving their deserts with PV and synthesising fuel (whatever that is: hydrogen, Sabatier methane, aluminium for burning) or just exporting that electricity along a 2m^2 cross section solid aluminium rod to the other side of the planet? Sure, plausible.
[0] I was going to say "and rockets", but then I realised we don't launch anything like as many rockets as we fly planes, so even then rockets might still be running on green hydrogen or methane derived from it.
Notably, SpaceX is making no visible effort to synthesize methane for their cans. The only gesture in that direction is an announced plan to buy a pre-fab methane refinery that could possibly be adapted to run Sabatier; but no hint at a solar farm to power it, or a place to put one. I guess they could build one across the border in Mexico? CH4 for Cape Canaveral is a separate problem. More likely the refinery will just purify mined LNG.
Solar and wind farms supplying international airports would probably need to send power via HVDC transmission lines. But, yes, the airports will need much more than just overage from the farms, and probably booster shipments of LH2 from farms in the tropics, besides. Imagine how big must be the project of refining, transporting, storing, and distributing kerosene to gates, today. Yet it is made almost invisible.
