Out of curiosity; what does a VFD that will drive a 10 HP 3 phase motor and be fed with a single phase circuit cost? I did not even know such an animal exists. VFDs to drive 3 phase motors with a 3 phase input were still becoming popular when I left the mechanical trades. Single phase to single phase was also available for small motors but not economical by any means. In my day when a 3 phase motor had to used on a single phase supply e used an open delta transformer connection. Same problem of loss as you all are discussing in this thread, just oversize the transformers and the primary circuit to match the load with the loss. Inspectors required that we well identify and have a warning label about the "wild leg" which was more than double the phase to ground voltage. You talk open delta to electricians today and they give you a blank look.
Most people do not know that a 3 phase motor will continue to run if one of the 3 legs drops out while running albeit kinda overheats. Do not try to start though. I once worked around a gippo sawmill outfit that used over size 3 phase motors for their loads (cheap on the used market) and they had a small single phase motor rigged to bring the big motor up to operating speed, unloaded, and then the switched on the 3 phase motor, then clutched in the load Burn up a motor, just go get another used one. Amazing what we ran into back in the 50s an 60s. Smaller cities did not have 3 phase power except in industrial areas.
After WWll, all of a sudden folks wanted air-conditioning. Any single phase motor over 5 HP was rare and expensive compared to 3 phase. Power companies did the open delta thing for years till distribution lines caught up. Then even 2HP and up became cheaper and more available in 3 phase. Hermetic motors then brought us a whole new set of problems. Back in those days a Refrigeration Tech had to be good electrician too.
Some day, when I feel like it, I will relate how we powered hermetic compressors for refrigerated trucks using 2 phase alternators driven off the engine and primitive speed/frequency control.
Ron