The below is assuming you are trying to place a VFD on the spindle of a knee mill for example.
OK, I have an extensive experience with VFD's as I've programmed, repaired and installed them in a previous job. First let me say that there is no such thing as "instant". What might seem like an instant forward to reverse change might be a .1s deceleration followed by a .1second acceleration in the opposite direction, or even faster.
OK, most older milling machines that I've seen that operate the motor directly on 3 phase without a VFD just open the forward contactor and then close the reverse contactor to change direction. This is called plugging the motor and causes excessive heating in the motor. If the motor is not specifically designed for this and you do it too many times in succession, you'll burn the motor up.
Next if you have VFD on your motor, and you press the change direction button, the vfd slows the motor down by reducing the voltage and frequency. When it gets to a stop it then accelerates in the opposite direction by increasing the voltage and frequency in the opposite direction. The whole process could take seconds or tenths of a second.
For those a bit more theory oriented:
When you start a motor across the line with a starter, the motor torque available is defined by the motor's speed / torque curve and can initially be 60% or less depending on motor design. All the while drawing 6-10X rated current. So during most of the acceleration time you have less than 100% torque available but you are drawing huge amounts of current. Where's all that power going? Heat in the motor.
When you start a motor on a VFD, the VFD accelerates the motor by increasing the voltage in proportion to the current and always keeps the motor below it's "breakdown torque" limit. By doing so the motor has 150-200% torque (possibly more depending on motor design) available for the entire time it's accelerating. All the while drawing no more than 150-200% of rated current.
Thus a VFD is THE fastest way to switch directions. A drawback is that when you are decelerating, the mechanical energy has to go somewhere, since it's not going into heating the motor. It increases the DC bus voltage of the VFD and the VFD must either slow down slower than the mechanical losses in the system or have some way to "waste" the energy. To waste the energy it can utilize a "Braking Resistor" to convert the regenerated energy into heat.
Example of a VFD advantage: I worked on a large fan application on a VFD that also had an across the line starter to be used in the event the VFD failed. This fan was a 400HP 4000V unit and it had a LOT of inertia. I program, tune and set up the VFD to operate the fan motor. I set the motor current limit to 100% and the accel time to 10 seconds. Starting the VFD, the motor accelerates up to speed in 10 seconds while staying under 100% current and 100% torque. Next step was to start the fan across the line to verify that it starts across the line as well. The starter picks up, draws 10X (1000%) rated current and starts accelerating. At 15 seconds later the motor has accelerated up to about 80% of full speed when the motor overload trips. The cause was the fact that the motor speed torque curve had significantly less than 100% torque until the motor got to 90% of full speed.
In summary, With a properly set up VFD and braking resistor connected to the VFD, A VFD will allow significantly faster direction changes than even plugging the motor would. It allows the motor to produce twice the torque (or more) than plugging the motor would.
Brian