The trend towards increasing the charging power of future e-mobility will challenge existing distribution power systems and raise grid utilization- and connection costs. Flywheel energy storage systems (FESSs) may reduce future power grid charges by providing peak shaving services, though, are characterized by significant standby energy losses. On this account, this study evaluates the economic- and technical suitability of FESSs for supplying three high-power charging electric vehicle use cases. Therefore, we initially investigate the impact of individual charging patterns on the required FESS capacity, the annualized costs, and the FESS efficiency. Based on these correlations, the economic and technical optima of FESS applications are identified for each use case: The supply of electric buses enables a cost-efficient operation at the technical optima of FESSs. In contrast, the economic suitability of FESSs considering electric last-mile delivery trucks or highway fast-charging is restricted to low recharging energy demands and high charging power of electric vehicles. Furthermore, a cost-efficient operation of FESSs at the technical optima requires either a reduction of flywheel costs or an increase of power-based grid utilization charges in the upcoming years.