Electron-spin qubits in Si/SiGe quantum wells are limited by the small and variable energy separation of the conduction-band valleys. While sharp quantum-well interfaces are pursued to increase the valley-splitting energy deterministically, here we explore an alternative approach to enhancing the valley splitting on average. We grow increasingly thinner quantum wells with broad interfaces to controllably increase the electron wave function overlap with Ge atoms. Quantum Hall measurements of two-dimensional electron gases reveal a linear correlation between valley splitting and disorder-induced single-particle energy-level broadening, driven by increasing alloy scattering at the Si/SiGe interface. We demonstrate enhanced valley splitting while maintaining respectable electron mobility, indicating a low-disorder electrostatic potential environment. Simulations using experimental Ge concentration profiles predict an average valley splitting in quantum dots that matches the enhancement observed in two-dimensional systems. Our results motivate the experimental realization of quantum-dot spin qubits in these heterostructures.