If you want to control a fan blower, then a phase control is most suitable for inexpensive approach. I have seen poultry houses running ventilation on single phase induction motors with U2008 circuit. Also the small fan blowers in the home pellet/wood burners, they all use shaded pole fan with phase control.
In theory, using the phase angle control, reduces the voltage on the motor thus the output torque is decreased with square of voltage. Also the required torque for fan is square related vs speed, so if you combine both voltage control of induction and fan load, then you have a good result.
Also the VFD, when used to power the fan is usually adapted to give a quadratic V/f output characteristics.
IMO, don't spend money on VFD for fan blower if it's not bigger than 2 kW.