If you happen to live directly over an open sewer or keep decomposing corpses under your floorboards, it's entirely possible that your cockroaches might be tracking the occasional pathogen on their sticky little feet, but their habit of incessant, cat-like grooming tends to rid them of contaminants long before they might scuttle over your ham sandwich.
In fact, testing shows that germs don't even stick to them that easily in the first place, so they're really only as dirty as whatever they're standing on at the time.
So, we know that roaches just aren't very dangerous... but we would still be better off without them, right? Sure, if you don't mind the wafting diseases that'll build up when we lose a major player in the process of decomposition. Cockroaches are also the primary predators of bollworm and armyworm, two of the most destructive pests of cotton, soybean, corn, cabbage and tomato crops in the United States and Africa.
Really, it's just a PR problem at this point. Maybe Pixar just needs to make a movie starring one of these guys.