> would move no air no matter how much power you dumped into it

Fun pedantic correction, it would move air via the Magnus effect [1], but of course it would be orthogonal to the direction you want it to be moved!

See the Turbosail [2] for a fun application of that effect.

[1] - https://en.wikipedia.org/wiki/Magnus_effect

[2] - https://en.wikipedia.org/wiki/Turbosail