Let's assume your robot arm example is about a frycook at a burger joint. I agree a robot arm isn't an effective way to replace the frycook, but a specialized system like Momentum Machines is developing[1] will be.
The automated fast food joint isn't a regular one with robot arms instead of people, it's a box the size of a small office that takes raw ingredients from a stockpile inside of it and creates fully assembled burgers, fries, chicken strips, and onion rings without any human interaction.
Automation hardware will strike a middle ground between specialization and reuse. Eg the deep fryer will be able to cook several different meals, but it will still only have 1-2 degrees of freedom for putting stuff in and taking it out. Similar story for the grilling surface, veggie chopping system, and the plating / packaging mechanism.
This is much cheaper, faster, and more reliable than truly general purpose robot arms. More importantly though, it takes dramatically less space than a conventional restaurant, so you can plop your company's food-making-box down in Times Square and actually make a profit, while everyone else is stuck four blocks away to break even on the real estate.
The stories will be different in different sectors, but in general I think the coming automation wave is a bunch of quantitative changes coming together to form qualitative ones like this. You could probably build a burger-maker a decade ago too, but the hardware and design know-how necessary have gotten orders of magnitude cheaper and more abundant, and so now it's actually happening.