The Baby Wiegold conjecture for characteristic finite simple quotients of free groups

Let $F_n$ denote the free group on $n$ generators. A subgroup $C\leq F_n$ is characteristic if it is preserved by every automorphism of $F_n$. The Baby Wiegold conjecture. For every $n\geq 3$, there are no characteristic subgroups $C\leq F_n$ such that $F_n/C$ is a finite simple group. This is presented as a special case of the Wiegold conjecture; the paper's results show that the analogous assertion fails for $F_2$.