In addition to the significant reduction in mechanical stress to drive components like gears, shafts, belts, bearings, etc., with most power tools at least, the primary beneficiary of an increased lifespan from a Soft Starter is the product ON/OFF switch. Think of the ON/OFF switch as merely 2 electrically conductive pads that, when contacting each other, close the circuit and allow current to flow to your electric motor, theoretically.
In many products it is the ON/OFF switch that is the first component to fail. Almost every time the ON/OFF switch is used, there is an inrush current (up to 400-500% of rating) that causes arcing and results in pitting and burn marks on the surface of the switch contacts. The greater this inrush current, the bigger and hotter the arc is, and the worse the pitting and burning is, eventually resulting in a switch that does not work.
Having spent 12 years in the electrical repair field I will tell you that switches, relays, and contactors, are some of the first components I look at when there is a related power issue. Have a look at the attached picture showing the difference between a new and used set of switch contacts.