The finite-codimension conjecture for prime ideals of Iwasawa algebras

Let $p$ be an odd prime, let $G$ be a uniform pro-$p$ group, and let $K$ be a finite extension of $\mathbb{Q}_p$ with valuation ring $R$. Write $KG=RG\otimes_R K$ for the Iwasawa algebra of $G$. The group $G$ is almost simple in the sense that it has no nontrivial closed normal subgroup with uniform quotient. A prime ideal has finite codimension if its quotient algebra is finite-dimensional over $K$.

Finite-codimension conjecture. If $G$ is an almost simple uniform pro-$p$ group, then every non-zero prime ideal of $KG$ has finite codimension.

This conjecture concerns the prime spectrum of Iwasawa algebras after excluding the prime ideals arising from closed normal subgroups with uniform quotients. The supplied text motivates the conjecture but does not state a resolution, so its status is left open.