Our bodies are not perfect or omniscient. We cough because it is evolutionarilly favored as a way to dislodge irritants, and viruses are evolutionarily favored

Our bodies are not perfect or omniscient. We cough because it is evolutionarilly favored as a way to dislodge irritants, and viruses are evolutionarily favored to cause that coughing response strongly in order to spread. Coughing too long seems like a very possible consequence of those.