In power quality applications I know that VFDs are notorious for causing AC harmonic distortion. Power companies are supposed to regulate their power to within a certain percentage of harmonic distortion for the power to be considered "clean". One of the issues in a modern electrical grid is as VFDs become more popular, the power companies are having a harder and harder time maintaining "clean" power. I have heard of instances where some industrial companies were producing such large amounts of THD stemming from VFDs, that once isolated to them, the power company made them install some elaborate isolation filters because THD affects the entire grid portion usually up to the next transformer that does a voltage step.
Things that spin, or get their clocking from the 60Hz wave, or sensitive electronics that do AC to DC conversion like a pure sine wave 60Hz AC to function efficiently and at a certain temperature range. The more TDH, the farther away form sinusoidal you get, and the worse things with motors and sensitive electronics run until they fail. It's the same principal as running things off a cheap generator. Some things won't work because of the high THD. it may be 120V, but the TDH is 15-30%, which makes the power unusable. Modern electric grid standards calls for <%5 THD, with 9% being considered excessive.
VFDs aren't the only culprit. "switching" power supplies like those in computers, TV's etc contribute to THD, but at a much lower level than VFDs. VFDs aren't bad, they just have to be filtered properly.