Brauer's conjecture on the resolvent degree of the general polynomial

For each $n$, let $\mathcal{P}_n$ be the parameter space of degree-$n$ polynomials and let $\widetilde{\mathcal{P}}_n\to\mathcal{P}_n$ be the associated cover parametrizing a root. The quantity $\operatorname{RD}(\widetilde{\mathcal{P}}_n\to\mathcal{P}_n)$ is the resolvent degree of solving the general degree-$n$ polynomial. Brauer's conjecture.

$$\operatorname{RD}(\widetilde{\mathcal{P}}_n\to \mathcal{P}_n)\to\infty\quad\text{as }n\to\infty.$$

The source presents this as a stronger statement motivated by the unresolved problem of proving that some problem has resolvent degree greater than $1$. Although the statement is attributed to Brauer in the surrounding discussion, no resolution is supplied here.