Answer
Flat wire wave springs provide a significant reduction in operating height compared to round wire springs. Because the load is proportional to $t^3$, using a thin, wide rectangular cross-section allows for the same spring rate $k$ with a much lower solid height $H_s$. In aerospace actuators, where every millimeter of axial space is valuable, a wave spring can reduce the spring cavity size by up to $50\%$. Furthermore, the flat surface provides a larger contact area, which reduces the contact stress $\sigma_c$ on the mating components, preventing 'coining' of the aluminum or composite housings often found in flight control systems.