Intercalation host compounds (IHC) are promising for selective ion removal from water. Recent theoretical developments have suggested that electrochemical desalination with IHC (nickel hexacyanoferrate (NiHCF)) electrodes could separate K⁺ and Na⁺ by a factor of 160. However, the experiments only produce a selectivity of around 3. In this work, we derive theory and a finite-element (FEM) model to investigate the origins of time-dependent selectivity suppression. The first results show that ion starvation can severely limit selectivity. Surprisingly, we also find that operations at low state-of-charge produce theoretical selectivity of 600, which is way above what was previously thought to be the theoretical maximum. Also surprising is that the main cause of low selectivity is that the constant-current overpotential disproportionally favors the adsorption of the ion that is less selected in the equilibrium state. By implementing short charging cycles near the depleted state with rest periods at the ends, we raised the time-dependent selectivity from 3 to 450. Even higher output selectivity could be achieved by combining IHC cathodes with membrane-less carbon anodes. In conclusion, the insights and methods derived here could enable highly selective ion removal at the device level for a wide class of IHC materials.