They do make a difference. However, not all VFD's will cause problems. You could take 100 motor-VFD combinations at a plant and run them all for 50,000 hours only to disassemble them and find evidence of pitting/fluting on only half of the motors. Prevalence depend on many characteristics including motor conductor lengths (whether the cables are impedance matched between the drive and motor). Mismatched impedance will increase reflected waves. Increase in reflected waves will increase the induced voltage measured on the shaft. The higher the voltage, the more likely an electrical discharge will arc from the shaft to the bearing. The electrical discharges will "machine" millions of tiny holes on the bearing track and burn the grease. Eventually the friction builds up and causes the motor to fail. Providing shaft grounding short circuits the path through the bearings so this machining does not take place. It does not eliminate the reflected waves, however.
Reflected waves can be studied more in transmission line theory, or fields and waves.
Not being an engineer, I picture a brush holder fitted to the bell housing with the brush rubbing on the shaft. Simple as that?
exactly that