[kabdib]

I was speculating about this with a friend the other day.

The problem is the battery recharge time is way more than the flight time. You need better than 1:1 for this to work.

Beamed power (sufficient to power something's lift) is going to have a scary energy density.

Maybe mechanical energy storage is the way to go; use counter-rotating flywheels that you can spin up rapidly, and then bleed off rotational power directly into the fans. Use a battery for powering control circuitry only.