  We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for
a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no
member of $\mathcal{G}$ contains a $k$-creature as an induced subgraph or a
$k$-skinny-ladder as an induced minor, then there exists a polynomial $p$ such
that every $G \in \mathcal{G}$ contains at most $p(|V(G)|)$ minimal separators.
By a result of Fomin, Todinca, and Villanger [SIAM J. Comput. 2015] the latter
entails the existence of polynomial-time algorithms for Maximum Weight
Independent Set, Feedback Vertex Set and many other problems, when restricted
to an input graph from $\mathcal{G}$. Furthermore, as shown by Gartland and
Lokshtanov, our result implies a full dichotomy of hereditary graph classes
defined by a finite set of forbidden induced subgraphs into tame (admitting a
polynomial bound of the number of minimal separators) and feral (containing
infinitely many graphs with exponential number of minimal separators).
