aircraft structures often being designed for strength rather than stiffness.
That's because aluminum, in this application, is naturally stiff for it's strength. I think you would find the same thing with wood in an airplane. Higher strength / higher density materials do not have this. If you tried to build the plane from steel you would be worrying about buckling everywhere.
This same issue shows up in a locost frame. An advantage for aluminum is that you could use a larger diameter tube which is longer and not worry about the buckling. I see this in the frame I am designing. There are places where a tube could be more then 50 times as long as it's diamter, which is much too slender. So more bays are needed to avoid this and it adds weight.
I don't think it's true that aluminum frame has no advantage, but an aluminum copy of a steel frame would have less advantage.
I think that fabric planes use steel frames because, in general, they were designed before good aluminum was available. WWII is when that started happening. I don't think 6061 was available until the mid 50's. For most people the idea of a plane made from aluminum monocoque was more attractive then a fabric plane. So in a way that's a more appropriate use of the material, Understanding the appropriate use is really a major key to a successful design.
Airplanes are designed with a fatigue life for pressure cycles and landings. A considerable number of major incidents are traced to these issues.