This study investigates the effect of tip-velocity constraints on system levelized cost of energy (LCOE). The results indicate that a change in maximum tip speed from 80 to 100~m/s could produce a 32% decrease in gearbox weight (a 33% reduction in cost) which would result in an overall reduction of 1%-9% in system LCOE depending on the design approach. Three 100~m/s design cases were considered including a low tip-speed ratio/high-solidity rotor design, a high tip-speed ratio/ low-solidity rotor design, and finally a flexible blade design in which a high tip-speed ratio was used along with removing the tip deflection constraint on the rotor design. In all three cases, the significant reduction in gearbox weight caused by the higher tip-speed and lower overall gear ratio was counterbalanced by increased weights for the rotor and/or other drivetrain components and the tower. As a result, the increased costs of either the rotor or drivetrain components offset the overall reduction in turbine costs from down-sizing the gearbox. Other system costs were not significantly affected, whereas energy production was slightly reduced in the 100~m/s case low tip-speed ratio case and increased in the high tip-speed ratio case. This resulted in system cost of energy reductions moving from the 80~m/s design to the 100~m/s designs of 1.2% for the low tip-speed ratio, 4.6% for the high tip-speed ratio, and 9.5% for the final flexible case (the latter result is optimistic because the impact of deflection of the flexible blade on power production was not modeled). Overall, the results demonstrate that there is a trade-off in system design between the maximum tip velocity and the overall wind plant cost of energy, and there are many trade-offs within the overall system in designing a turbine for a high maximum tip velocity.