You can --and often do-- connect a standard induction AC motor to a VFD. But the VFD does not provide a sinusoidal output signal to the motor (it uses SCRs or IGBTs to generate a variable-frequency sinus-looking signal from a DC voltage) and it includes many harmonics that can proove harmful to a standard motor (over the long term), tending to overheat it especially at low-frequency runs.
So the industry provides what is known as inverter-duty motors, with special insulation and more air-cooling capabilities, for pumps and fan applications.