Static converters have a place. . .they are the least expensive, initially.
I had one that I was called to troubleshoot. A 240V 3? roof top AC had lost a compressor, which had been replaced. Now, the new compressor just buzzed loudly, when energized.
The static converter "start" capacitor bank (about a dozen electrolytics, as I recall) were all blown. The "run" capacitor bank tested OK. I put in the new caps. . .and the compressor still buzzed.
After a period of self reflection, I crawled into and over the new compressor to read it's label. Lo and behold, the replacement was a 480 Volt unit! I locked out and tagged out the power, and left the news with the owner. Once the compressor was replaced again, the RTunit worked fine.
I guess my point is: The "3rd phase" is a capacitor shifted leg from the single phase. The timing of the 3 phases is not even which gives rise to additional vibration and energy loss. The motor will have a more stressed life. If the motor is automatically run, like my RTU example, loosing the start capacitors can leave the motor single phased.