Unfortunately the problem with electric aviation isn't the storage tech. Although having superconductors around would make the ground infrastructure nicer, if the current density limit works out.
That's part of the problem, as is the fact that batteries don't get lighter through the flight. The energy infrastructure on the ground is the thorny bit, though.
Getting enough energy into enough planes fast enough at enough airports to make a dent. As a guide to the order of magnitude of the problem, consider that a 747 needs roughly 100MW to stay airborne.