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.