The major goal of the rubella vaccine is not to protect the recipient from German measles. The illness is very mild, slightly worse than the common cold, with only rare side effects. However, if a pregnant mother develops rubella, she is at increased risk of having a miscarriage. In addition, her baby is at increased risk of congenital rubella syndrome, which includes blindness, deafness, or mental retardation, and an increased risk of death.
Before the rubella vaccine was developed, there were regular epidemics of rubella in the United States. One epidemic from 1964 to 1965 led to an estimated eleven thousand miscarriages, two thousand infant deaths, and over twenty thousand infants born with congenital rubella syndrome. By comparison, in 2000, only six cases of congenital rubella syndrome were reported, mostly from immigrants who did not receive the vaccine in their country of birth. So if we stopped vaccinating against rubella, we would see a large increase in the number of birth defects due to congenital rubella syndrome as well as a large increase in the number of miscarriages.