That is a non sequitur. The most dangerous illness associated with fast food (poor nutrition aside) such as E. coli[1] and Hep A[2] are most readily attributed to ingredient suppliers, not improper food handling.
That doesn't mean that labour aren't a more frequent source of food-borne illnesses, just not the most serious cases. I'm not likely to die from someone sneezing in my food, but I don't want to catch what they have nonetheless.
True, but with a full automatic system to convert those ingredients to food, you could add a test step, where you filter out the contaminated ingredients.
And who handles the ingredients improperly? Doesn't refrigerate them sufficiently? Uses expired ingredients? Fallible humans. Lets remove them from the equation.
Robotic slaughterhouses would still have problem keeping fecal matter out of meat. The best way of preventing most food illnesses is radiating the food, but our irrational society won't go for that.