Where automation clearly pays off today
Robotic automation earns its keep fastest where the task is high-volume, repetitive, and physically demanding or hazardous, and where the environment can be reasonably controlled. Palletizing, automotive spot welding, and pick-and-place on a well-defined production line have justified robot investment for decades because the return on investment is straightforward to calculate: a robot working three shifts without breaks, sick days, or injury claims, doing a physically punishing task consistently, pays for its capital cost within a few years in many established use cases.
Automated storage and retrieval in warehouses is a newer clear win, driven partly by e-commerce order volumes that would be brutally expensive to fulfill with proportionally scaled human labor, and partly by labor markets where warehouse turnover and availability have become genuinely difficult problems for employers, independent of wage levels. In both cases the economics work because the task is well-defined enough that a robot's narrower flexibility isn't actually a disadvantage.