Why don't we see more Soft-wing Ground-Gen AWE systems without pumping-cycles?

Hi @jellepoland good to see you here!

Something like W&I rotating designs already exists and also something like «The Pyramid» could easily be implemented using soft kites.

I think the question is slightly wrongly worded. You always want the best possible performance. So the quedtion is rather; why would a soft wing be better suited for a certain application.

From where I stand, soft wings have lower aero efficiency but this may largely be offset by tether drag anyway to an extent where it doesnt matter much. Next you have handling issues, if said soft kites are maybe bigger and harder to «catch» than a comparable soft kite. On the positive side though, you may get more energy for a given mass, and it may scale to bigger sizes.

These are all quite fuzzy subjects so its hard to say which is the better choice.