Rossmann's pole-existence conjecture for algebra zeta functions

Let $\mathfrak{O}$ be the coefficient ring and let $A$ be a finite-dimensional $\mathfrak{O}$-algebra. Write $\zeta_A(t)$ and $\zeta^{\lhd}_A(t)$ for its subalgebra and ideal zeta functions. Rossmann's pole-existence conjecture. Both $\zeta_A(t)$ and $\zeta^{\lhd}_A(t)$ have a pole at $t=1$. Equivalently, the coefficients of either zeta function do not $p$-adically converge to $0$. The conjecture is known for residually nilpotent algebras, but remains open for general finite-dimensional $\mathfrak{O}$-algebras.