From wikipedia[0] "it is possible to mechanically recharge the battery with new aluminium anodes made from recycling the hydrated aluminium oxide". I've found a few papers regarding recovery of aluminum from aluminum oxides, but I don't have the background to interpret them with an eye towards that process's impact on the overall efficiency of the battery.
Production of aluminum metal from aluminum oxide is hugely energy-intensive. Aluminum plants often have an on-site utility-size power plant to provide the electricity. Is this same energy needed to recycle the oxide from the batteries? If so it seems like a non-starter, maybe unless it could be done with solar generation.
The real question here is the ratio of energy delivered over the life of a fresh anode as it is fully converted to aluminum oxide, to the amount of energy required to turn that same aluminum oxide back into a pure aluminum anode.
And that must and is changing. Green transport is predicated upon a green grid.
Additionally, a “wasteful” process, like electrolysis of water to make hydrogen, can be usefully inserted at onsite wind generation sites for when the grid isn’t requiring/buying vs sitting idle. When you see large wind turbines stopped and you know that there is a constant stream of wind at 50m above that ridge line it’s simply because the grid is not buying atm. I’m positing that aluminum air batteries are viable for aviation for the same reason.
There is no "recharging" an aluminum-air battery, you add the energy back through recycling (smelting) it.
One of the big synergies is with renewables: With the right industrial process, you can treat this smelting process as a way to dump excess energy in peak production times.
It's the same idea of green hydrogen. Only hydrogen allows you to use pipelines instead of physically hauling everything. You also don't have to worry about the battery physically gaining weight as you fly.
I remember 20 years back, hydrogen was going to be it. There were prototype cars manufactured, calls for hydrogen fueling stations to be built, everyone scrambling to get on the hydrogen train. Then it all just fizzled out. It was probably one of the promised techs I most wish had lived up to the hype.
[0] https://en.wikipedia.org/wiki/Aluminium–air_battery