Simpson's motivicity conjecture says that for any rigid, flat irreducible connection $(V,\nabla)$ on a smooth complex variety $M$, there exists a proper smooth morphism $f:X \to M$ s.t. $(V,\nabla)$ is a subquotient of the Gauss-Manin connection $R^if_*\mathcal{O}_X$.

Here is my question. Why does the above conjecture require the rigidity of the connection?