If $R$ is a simple Artinian ring with simple module $M$ then $M$ is finitely generated as an $\mathrm{End}_R(M)$-module. This is usually proven in an indirect way: By Artin-Wedderburn-Theory we may assume that $R = \mathcal{M}_n(D)$ is a matrix ring over a division ring $D$, and $M = D^n$. Then it is obvious that $M$ is finite dimensional over $\mathrm{End}_R(M) \cong D^{op}$.
Is there a more direct / more elegant way to show that $M$ is finitely generated over $\mathrm{End}_R(M)$ which avoids matrix rings? Are there more general conditions on $R$ and $M$ under which the conclusion remains true?