I did some experimentation on topic with a ceiling fan motor (wings detached) with rated power 80W stamped on the device. The motor is a permanent-split-capacitor motor intended for 230V / 50Hz. My digital multimeter displayed exactly this voltage for the mains connection. The voltage measured across the auxiliary winding was 226V while running the motor normally in the original shape. The drive was a Siemens Micromaster 410 rated for 0,37kW.
I measured the temperatures of the motor rotating drum with the original setup (using an IR meter). The temperatures varied between about 50 centigrades on the outer edge of the rotating external drum and about 55 degrees near the axis after running the motor for more than an hour
I then removed the capacitor and connected the main winding and the auxiliary winding at one end to two output connectors of the drive and the common point of the windings to the third connector so that the direction of rotation did not change
I measured the temperatures after running the motor again for more than an hour with the three-phase capacitor-less drive-based setup; the measured temperatures remained the same, and at least, the temperatures were not higher than with the original setup
the temperatures with the three-phase drive-based setup was highest with the highest rotation speed and frequency tested (50Hz)
the noise with the drive-based three-phase setup was higher, but mainly due to noise from the switching frequency (2kHz in this case)
the starting torque was considerably stronger with the three-phase drive-based setup than with the original single phase capacitor-split setup; the torque difference was even larger at lowest frequencies tested (20Hz)
Overall, the idea seems plausible for further testing with the power range of typical ventilation fans used in single residence houses. The most critical problem that might arise is the PWM switching noise. Also, the voltage stress caused by the spiky PWM waveform might need consideration depending the motor. The tested setup would solve the problem of very low starting torque related with single-phase permanent-split-capacitor asynchronous motor run at reduced frequency by an inverter drive. An ideal drive for the purpose would allow adjustment of effective voltage between at least two output terminal pairs and the phase angle difference between the same two, which standard drives do not support.
Update (21st December 2020):
I tested the same setup (three-phase inverter drive for a single-phase run capacitor ceiling fan motor) with the modification for true 90 degree two-phase circuit. The latter circuit was made up of two identical isolation transformers 400V/230V. The primary windings were connected mirror symmetric between the connectors feeding the main winding and the common 3rd connecter of the drive. The secondary windings were connected in series. Since the drive outputs the effective voltage of 230V, the transformer cores have a wider margin for magnetic saturation than with the specified primary voltage (which is not necessary, but might provide further options for selection of drive frequency vs. voltage curves for enchanced low rpm torque control). Thus, the result voltage for the starting winding is also about 230V at nominal frequency (50Hz).
I did the same temorature measurements as above. This time the temperature of the motor casing remains well below 45 centigrades. This is lowest of the three cases tested, which is no wonder, since the motor is now driven with ideal two-phase alternating voltages of 230V plus minus something with the phase angle separation of 90 degrees at any frequency produced by the inverter drive (the true effective voltages will follow the frequency as usual).
So I concluded to adopt this circuitry for driving the ventilation fans of my house with synchronised but variable speed. This is now a true two-phase system. I used to have the drive to feed a single-phase voltage with a variable frequency to the run-capacitor split-phase fan motors, but I was dissatisfied with the approach, since the starting torque was very low especially at reduced rpm and the capacitors tended to degrade within a few years creating even worse behavior. Now, I can remove the capacitors of trhe fan motors and feed the auxiliary coil directly with this phase-shifted voltage. True three-phase motors are difficult to get for such relatively small house-oriented ventilation fans. I prefer asynchronous fan motors over EC ones due to fewer problems with wear-induced tonal noise and lower cost, even though power consumption is somewhat higher.