Enabling "axial only" geometric stiffness on the support structure is expected to lower the tower natural frequencies, an effect known as "gravitational destiffening". Why can't I see this effect in my Campbell diagram?
Gravity is disabled by default in the Campbell Diagram and Linearisation calculations for onshore and fixed offshore turbines. The gravity is disabled to remove periodicity in the rotor i.e. so that the linear system is the same at any azimuth angle, and a linear time invariant system can be generated for control design.
This means that the "axial" (vertical) load in the vertical tower members is zero (or close to zero) due to missing gravity load. The "axial only" geometric stiffness is proportional to the axial load in each member. So the geometric stiffness has no effect on the vertical tower members without gravity load.
To observe the gravitational destiffening effect, you can enable the gravity in "calculation options". However this will also introduce unwanted periodicity into the system.