Agitator dogs are prit'much a wear-part akin to tires on a car.
I think there were other brands of dryers before 1958 that had auto-dry but in some cases it operated at only one dryness level with quite a high-temp cut off point.
Kenmore had an automatic water level function on the Lady Kenmore, apparently only for half a year in 1961. It's in the Spring/Summer catalog. The 1961 Fall/Winter catalog shows the same button layout on the panel but *with* a water level control and the description says the user selects the level. Per the 1961 Spring/Summer catalog description: "Automatic water level never wastes a drop . . never needs setting either. Provides just enough for any size load from 2 to 10 lbs. Even adds more water if you add more clothes." I don't think anyone here has yet found any tech details on how it worked.

