The real reason why many humans consider cockroaches (and ants, wasps, rats, some grasshoppers, ...) as "annoying" is that they are so successful. These kind of animals are generalists, which don't depend on one single food source, have the ability to hide, often run fast and fly, survive very high and low temperatures, reproduce fast, are often intelligent as individual or state. The result is that they become our serious competitors for food and living space.
I actually respect them (this is the "Fascinating" not "Annoying" insects community), but in some caes have to fight them myself.