We investigate the THz emission characteristics of ferromagnetic/non-magnetic metallic heterostructures, focusing on thin Fe/Pt bilayers. In particular, we report on the impact of optimized crystal growth of the epitaxial Fe layers on the THz emission amplitude and spectral bandwidth. We demonstrate an enhancement of the emitted intensity along with an expansion of the emission bandwidth. Both are related to reduced spin scattering and higher interface transmission. Our work provides a pathway for devicing optimal spintronic THz emitters based on epitaxial Fe. It also highlights how THz emission measurements can be utilized to characterize the changes in out-of-equilibrium spin current dynamics in metallic heterostructures, driven by subtle structural refinement.