Strong circle generator complexity conjecture

Let $K_n$ be the set of inequivalent character tables of size $n$. Let $\mathbb{E}(K_n,N_{\mathrm{cls}})$ and $\mathbb{E}(K_n,N_{\mathrm{fus}})$ denote the average circle generator complexities of the class and fusion algebras, respectively.

Circle generator complexity conjecture (strong version). The average circle generator complexity of class algebras is smaller than the corresponding average for fusion algebras:

$$\mathbb{E}(K_n,N_{\mathrm{cls}})<\mathbb{E}(K_n,N_{\mathrm{fus}})$$

for all $n>6$.

This conjecture formalizes the observed tendency that class-algebra circle generator complexity is smaller than fusion-algebra circle generator complexity. The source provides numerical evidence but no proof or resolution.