I think you are correct that it is somewhat a philosophical question -- the designer chooses the intent and then has some leeway to accomplish it. If certain members are too stiff, they will carry load and can foil the intent...
Monocoque means stressed skin. If you aren't carrying load through the skin, it isn't a monocoque structure. Semi-monocoque is mostly a compromise that recognizes that you can't carry a large load through thin skins without buckling -- so stiffeners are added to help carry load and prevent buckling.
Think of aircraft structures before monocoque designs existed -- wood and fabric or metal tube and fabric prevailed. Some were externally braced - strut and wire. In this era, the skins were typically fabric. From a structural analysis / design perspective, the skins were neglected. As an engineer, you ignored the skins and analyzed the loads on the spar, truss, frame, or whatever structure was hidden by the skins.
Today, structural approaches can be much more complex. They likely aren't a pure monocoque or semi-monocoque structure -- but you also can't ignore the skins.
You might consider a North American T-6 Texan as an example. Just outboard of the main landing gear, there is a blister that wraps around the airfoil. This blister covers an external flange where the outboard wing panels are bolted to the inboard wing panels. This allows the stresses from all the way around the skin to be transferred to the inboard section.
The inboard wing panel has a continuous upper skin that carries loads from one side to the other. The lower skins have large fuel tank doors that I believe are similarly installed and also carry substantial load. Consequently, the bending moments of the wings are never reacted to the fuselage -- they are handled internally to the wing itself. The fuselage sits on top of the wing. That allows the wing-fuselage joint to handle much more straightforward loads.
Likewise, the aft fuselage of the T-6 is a semi-monocoque design, but the area around the pilots is a steel tube structure where the large skin panels can be removed for maintenance.
The wings of many aircraft of that era are attached in similar ways. The Douglas SBD-5 and
DC-3 come to mind.
Search for 'Erection and Maintenance' manuals. Compare these aircraft to those with non-monocoque structures -- say a Stearman or Cub.
You say that the wings can not take advantage of a progressive / geometric strength increase. I presume you're referring to the fact that the spar of a tapered wing gets thicker at the root because the airfoil gets thicker. I assure you it gets thicker in material thickness as well. But so do wing skins. See if you can find a reference for the skin thickness at the root of a 747 wing vs. the tip -- or any other similar aircraft.
Small aircraft have much lower flight loads on them. However, non-flight related loads stay about the same. Things like hail damage, walking on a wing, maintenance, lightning, and hangar rash may all require a skin thickness larger than the flight loads would suggest. Likewise, material availability (fixed and discrete thickness of sheet metal) and manufacturing processes (minimum thickness of machined panels, or minimum thickness for a desired flush-set rivet) may all determine the minimum gauge of the skin.
Stress analysis for a small aircraft wing may suggest that you only need .003" Al skins near the wing tip -- but who is going to skin their airplane with aluminum foil? Try pushing that around a hangar, tying it down, or simply leaning on that wing.
I have read that the skin thickness of a popular homebuilt aircraft is set by the minimum thickness for a #3 countersunk rivet. Home builders can not reliably and consistently drive smaller rivets, so you use what works.
All of these factors can be considered minimum gauge.
If your minimum skin thickness is not set by flight loads, then the skin is not going to be heavily loaded. You also won't have a lot of opportunity to reduce weight out of the structure.
Super-light aircraft like Solar Impulse 2 actually go beyond the point where stressed skin makes sense. It is a super high-tech tube and fabric design with space age materials. In their case, it is likely that almost every aspect of the structure is sized by stability (buckling). So the internal structures form a truss of lightweight members with large sectional second moments and the length of any truss member is kept pretty short. The skin is just a layer to keep the wind out.
These extreme approaches are great for breaking records, but they won't handle the abuse of a working aircraft over a 20-50 year service life. Some of those non-flight loads can be ignored if your aircraft only needs to fly for a very short life under extremely controlled conditions.
Rob