Let $n$ be a positive integer. It is well-known that a method to realize irreducible $\mathfrak{S}_d$-modules is to construct the so-called Specht modules $S^{\mu}$ which are submodules in the so-called $\textbf{permutation modules} \ \ M^{\mu}$ (see, e.g. Bruce E. Sagan's book ""The Symmetric group"")

Schur-Weyl duality supports such a view of point. Namely, the double centralizer property gives that $((\mathbb{C}^n)^{\otimes d})_{\mu}\cong M^{\mu}$ for all dominate weight $\mu$, i.e. $\mu$ is a partition, thus we may find all $\mathfrak{S}_d$-irreducible modules modules by decomposing $M^{\mu}$.

My question: Are there other reasons which explain why irreducible modules are in permutation modules? Thanks!