Your correct. I was trying to keep it simple. Looking at the sine wave on an oscilloscope would verify the phase shift before getting back into the 120 degree area which is never perfect like a transformer conversion in industrial environments which also fluctuates for a few milliseconds at startup.Just a note....... (if it even makes any sense)
Static converters do work but they are not perfect by a long shot. You only get 2/3 the rated HP and the motor will run hot even at that. You also will need a start cap momentarily in the circuit to get the thing running Remember single phase is 240V center tapped to get the neutral and 120V across either winding to neutral. That makes the waveform 180 deg out of phase NOT the 120 deg a 3 phase motor is looking for. The manufactured leg out of the caps will float all over the place as load goes up and down. For most applications a rotary converter or VFD will be a better choice.
Motor start up has a lot of phase issues no matter what gets it going.
What's also interesting is back in the day when working in the machine tool world as a CNC tech we had occasions during the day when one phase of the 460 would drop out plant wide. There were a couple hundred CNC computer driven machine tools in operation at that time. During the interruptions of the three phase, the machine tools never suffered any issues. They continued to operate as usual.
Lasted for several months even on weekends when the majority of the CNC machine tools were shut down.
One Sunday, went in with the minimum of employees on the job on machine tools, with only the heat treat facility open for business, and it was still happening.
With permission started shutting down every operation. When the situation corrected it turned out to be a three phase heat treat draw furnace element that had broken loose and went to ground that was on a timer. That is why the problem came and went.
Three phase doesn't need true 120 degree phase separation to operate. That is the optimum. It just needs a differential which puts it back to your observation that the phase converters are inefficient and the reason why.
BUT! They are cheap and will make 3 phase motors operate. Other systems at higher prices are better.