Polynomial minimal separators or bounded hole length for induced-minor-free graphs

Let $G$ be a graph. A clique cutset is a clique whose deletion disconnects $G$, a minimal separator is a minimal vertex set separating two vertices of $G$, and a hole is an induced cycle of length at least four. An induced minor of $G$ is obtained by deleting vertices and contracting edges.

Polynomial-separator or bounded-hole conjecture. There exists a polynomial $p$ and an integer $k$ such that if $G$ has no clique cutset and does not contain $K_{2,3}$ as an induced minor, then either

$$|\{S:S\text{ is a minimal separator of }G\}|\leq p(|V(G)|)$$

or $G$ has no hole of length at least $k$.

This proposes a structural dichotomy for graphs excluding $K_{2,3}$ as an induced minor: graphs without clique cutsets should either have polynomially many minimal separators or have uniformly bounded hole length. The source presents this as an open question; no resolution is given.