The goal is to run a 3ph AC motor with either high or low voltage inputs. The motor would be wired for a specified voltage and the controller drives a single output regardless of the line voltage. I looked at VFDs but I can't seem to find a unit with a variable line input. Does such a device exist?
It seems unlikely that you will find such a VFD, but it may be worthwhile to look carefully at the protection specifications and setting ranges if the UV and OV protections can be set by the user. The cost of the 400 V class models is sufficiently more than the cost of the 200 V class. That would make 400 V class products designed to accommodate 200 V class operation non-competitive in the market. Manufacturers are not going to offer products that are not competitive. Even if it costs little to make a 400 V VFD capable of operating in the lower range, manufacturers would not be likely to do it. However there may be a market for VFDs that can tolerate extreme voltage dips. So some manufacturers may have that capability that is not advertised as dual voltage capability.
This was done years ago with some brands of solid state soft starters. You could apply any voltage higher than the motor voltage and it would limit the output to the programmed lower level to match the motor. But soft starters are roughly 97% efficient, meaning you lose 3% of the power as heat, so they can't be enclosed without a lot of ventilation. Soft Starters are enclosed all the time of course, but because we use a bypass contactor, however using a bypass contactor then eliminates this possibility. So the product concept died about 20 years ago from lack of interest due to the inherent problems. Nobody has pursued it again most likely because transformers will always be cheaper.
I should note that soft starters are not "drives" in that they can't change the speed, just the voltage. With "drives" like VFDs, the problem described above makes the concept untenable; the DC bus voltage would be far too high and likely cause damage to a lower voltage motor.
To address another aspect:
Figure 1. A VFD internal diagram. The DC bus consists of the DC power-rails from the capacitor to the top and bottom of the transistor switches.
It should be clear from Figure 1 that the transistors will apply the full DC bus voltage to the motor. If running a 220 V motor, which would expect to see a phase to phase peak voltage of 220√2 maximum, on a 460 V supply it would see the DC bus voltage of 460√2 instead.
While the average voltage and current could be controlled in the VFD algorithm, the peak voltage could not. It is very unlikely that the winding insulation of a motor rated for 220 V could withstand that level of over-voltage.
there are dual rated drives but the output voltage is what the input voltage is. that means you would need to change the motor wiring according to the drive supply source negating the convenience of changing voltage input to a static motor.