Variable Frequency Drives (Named AC drive, variable speed drive or frequency inverter, shorted for VFD) can alternatively be chosen based on Torque (Nm) requirements. The basic thinking is that Torque is related to current (amps). Furthermore you need to take into account, for this approach is Nominal/Maximal Torque to ensure that especially starting Torques which are typical to each application can be generated. Applications are very quite distinctively, so a variable frequency drive controlled fan application is quite different than a hoist operation but the logics is applicable in the same way.
Using Power (kW) is in fact less logical if you look at the definition of Power (is equivalent to delivered Torque at a fixed speed). When this is applied to a variable frequency driven system, the power calculation actually varies quite dramatically over the complete speed range although you would be applying this to the same components.
There combination current versus frequency is a bit more tricky since the current is the main component for the magnetic field in the motor. In fact if you dive into details you will find out that the Torque being delivered to the driveshaft is in fact caused by the difference in speeds (slippage) between the frequency of the electrical field rotation and the actual rotation speed of the shaft.
This means that at VFD drive speed shaft rotation 0, Torque can be generated while the speed of the rotation of the magnetic field in the motor is already running. What is also true is that the Torque can be quite high (ie max torque) at driveshaft speed is 0. This is why AC VFD systems can be used in motion and traction applications.