Why would there be no cure for the common cold?

Lack of vaccine: Vaccination is the most effective way of controlling infectious diseases. However, it is not feasible to produce effective vaccine against "cold, " because too many viruses are involved.

Cold: There are over a 100 viruses that cause the common cold. Viruses can mutate. Severity of common cold symptoms are usually not extreme and the disease is usually self- limiting. These are reasons why it wouldn't be a high priority to look for this cure.