SuperTurbine ™, AirLoom, Airborne Seaborne Wind Energy Systems, and perhaps some other systems can be seen as AWE / HAWT hybrid systems, although they do not have much in common.
Generally they are designs using the air to borne a part of the structure without really fly. Perhaps some key could be found in order to mitigate the cantilever effect of HAWT and reach higher altitude while sweep more.
See also
We could add AWE / VAWT devices.
Some elements from AWE (inflatable wings or blades, use of a gas lighter than air like in the sketched device below) could perhaps equip non-flying wind turbines.
From the geodesic dome to VAWT:
From the geodesic dome shaped VAWT to a half dome VAWT in order to achieve more stability with a large (rotating) basis, working like a carousel.
Then from half dome VAWT to the Wind inflatable half dome which would use inflatable shapewave® blades in order to lighten the structure which only adds ropes to the blades. The carousel itself becomes relatively light (an idea for carousel-based AWES?), the only heavy elements being the generators. Thus if it works, it could be a portable wind device, even at high scale, and particularly suitable offshore.
Oooooh cool
I wonder could we morph that further…
Morphed half Dome design
Let’s say Have 2 horizontal lines around the dome at ~ 2/3 height.
Between the 2 lines have many blades linked to the lines at their spanwise ends.
Effectively making the 2 lines more of a ribbon
Let the ribbon deform🎗️
Downwind the ribbon loop of blades is perp to wind (blade spanwise vertical) giving drive
Spinning the dome
Upwind the ribbon 
loop of blades is spanwise to wind flat horizontal giving lift
Holding dome form.
How much control does it need?
Worth an experiment / SIM /…?
Version with rigid blades, which is not really different, but perhaps more suitable if we can use the geodesic dome shaped configuration:
Interesting proposal from @Rodread on the comment just above.
A preprint of Wind Half Dome (DOI: 10.13140/RG.2.2.14276.33929).
A slightly clearer sketch:
A publication investigates the deformations of inflatable profile:
From the Abstract:
As the flow speed is increased the aerofoil deforms significantly around its trailing edge, resulting in a negative camber and a loss of lift. The loss of lift is ameliorated by increasing the inflation pressure but at the expense of an increase in drag as the aerofoil bulges into a less aerodynamic shape.
Perhaps some rigid elements like rods could mitigate the deformation. But things look to be difficult at high scale. Inflatable blades or wings are almost non-existent in the fields of wind energy and aviation, with a few marginal exceptions. Perhaps some possibilities could occur for drag-based Savonius kite turbines where the profile is less demanding.
Is it also the case that fat foils inflated are generally less affected by the trailing edge bulge issues?
Cool concept Pierre
Looks like a great design to test shapewave bonding between skins to hold foil form
Always liked an arch design
It’s likely the arches would be noticeably deformed in practice, with material pulled towards a downwind bias to balance the aero forces
I suspect the resultant profile would be Kinda like half a water balloon (a breast profile shape (surely I know a better description))
90 Deg rotated
Downwind being the underside
Must be too late at night for me to be commenting online 
What worries me about this design is that the topmost parts cold be travelling slowly
And at scale might become very flexible
Worth investigating though
I hinted at this with the guess below. Yes, a thicker profile could be more favorable, but with probably less efficiency, and still the need to stiffen the trailing edge.
In addition, the profile being larger, its span will be greater (scaling effect), which will increase the deforming effects of the wind, particularly in the middle.
There is therefore little chance that this solution is really one.
Concerning the other aspects of the dome, there are the reservations that you express. I would add the tendency of the carousel to dive downwind.
In addition, brief calculations show that this would require (for rigid profiles) industrial quantities of aluminum or other, hence the unexpected but minimal advantage of a flywheel effect for a limited time.
With inflatable profiles we will have deformation problems, hence loss of efficiency.
