While some of the most elegant applications of topological insulators, such as the quantum anomalous Hall effect, require the preservation of Dirac surface states in the presence of time-reversal symmetry breaking, other phenomena such as spin-charge conversion rather rely on the ability for these surface states to imprint their spin texture on adjacent magnetic layers. In this Rapid Communication, we investigate the spin-momentum locking of the surface states of a wide range of monolayer transition metals (3d-TM) deposited on top of Bi2Se3 topological insulators using first-principles calculations. We find an anticorrelation between the magnetic moment of the 3d-TM and the magnitude of the spin-momentum locking induced by the Dirac surface states. While the magnetic moment is large in the first half of the 3d series, following Hund’s rule, the spin-momentum locking is maximum in the second half of the series. We explain this trend as arising from a compromise between intra-atomic magnetic exchange and covalent bonding between the 3d-TM overlayer and the Dirac surface states. As a result, while Cr and Mn overlayers can be used successfully for the observation of the quantum anomalous Hall effect or the realization of axion insulators, Co and Ni are substantially more efficient for spin-charge conversion effects, e.g., spin-orbit torque and charge pumping.