Oriental cockroaches feed on dirty things, and you will likely find them on garbage, decaying organic matter, rubbish, and discarded tins. Since they have a habit of harbouring in unsanitary damp areas, they are likely to spread filth from these sources to your cooking areas, dishes, utensils, and other clean surfaces.
Also, these cockroaches produce stinky secretions in their bodies that, if released in food, can affect their flavours. If the roach infestation issue in your property is too high, certain areas may begin to smell because of their secretions. Moreover, it is not uncommon for disease-producing organisms like bacteria, protozoa, and viruses to be found on their bodies, which means if they contaminate your food, you may contract diseases like food poisoning, dysentery, diarrhea, etc.
Also, their excrement and cast skins contain allergens that may trigger allergies in some people.