Extremality conjecture for irreducibles of uniform matroid monoids

Let $M$ be a matroid of rank $k$ on $n$ elements, and let $d4c9_p(M)$ denote its associated monoid. Write $\operatorname{Irr}(\mathcal{Q}_p(M))$ for the set of irreducibles of this monoid. Extremality conjecture. The number of irreducibles of $\mathcal{Q}_p(\operatorname{U}(n,k))$ is an upper bound for the number of irreducibles of $\mathcal{Q}_p(M)$, where $M$ ranges over all matroids of rank $k$ on $n$ elements. The conjecture was checked for all matroids on at most four elements, but remains open in general.