AFAIK the best reason to use a VFD drive on a pool pump is that you go from a single phase motor to a 3 phase one. The single phase motor is generally a lot lower efficiency in converting input AC power to actual shaft power over the 3 phase unit, so the overall efficiency of having a fixed 3 phase drive, and a 3 phase motor, of the same RPM and power output, is a motor that runs a whole lot cooler, so thus less of the input power is going out as heat in the windings and core losses. Your typical pool pump motor runs around anything from 600W to 1.1kW, though the efficiency is not always stated, and they run really hot. Swap out to a 3 phase motor in the same frame, and you find efficiency goes up from around 70 odd percent to well over 90 percent, just from the lower losses in the core and windings.
For a pool pump, where all parts, automatic cleaner, filter, heat pump, skimmer and returns are all optimised for a very small variance from the full power of the standard motor, and you will probably see around 10% savings in power from having the fixed frequency inverter and a 3 phase motor there. Pool pump motor you can retrofit, they mostly use a standard IEC flange size, though often they use a special shaft, but that is easy to fix just by swapping in the 3 phase motor body, and toss the end caps, rotor and the old pump single phase windings. Reuse the rotor, it likely will be a perfect fit, as they do use standard sizes in the motors, to gain advantage of industrial production. Take a thermal image of a single phase motor versus a 3 phase one, running any load, from zero to full, and you will always see the single phase one runs a lot hotter, especially with lower load.