Maschke's theorem tells us that any representation of a finite group $G$ can be decomposed into a direct sum of irreducible representations. The proof does make intuitive sense to me (Intuition behind Maschke's theorem), but my question is really about why we should expect it to be true in the first place.
Sure, we can do some explicit examples (perhaps a most obvious starting point is the standard permutation representation of $S_n$, which has an obvious invariant subspace $\{(x,x,\ldots, x) \in \mathbb C^n: x\in \mathbb C\}$, and almost as obvious complement subspace $\{(x_1,\ldots, x_n) \in \mathbb C^n: \sum x_i = 0\}$), and perhaps one has already seen the result for abelian groups over $\mathbb C$ in the guise of linear algebra: Matrices commute if and only if they share a common basis of eigenvectors?.
However I wonder if there is any other point of view that makes Maschke's theorem feel "inevitable"...since right now, it just seems absurdly powerful/magical.