Yes there is still a cloth diaper service in business and they do still provide the service of cleaning and delivering more clean cloth diapers.
Most cloth diaper services closed down when they stopped being as profitable or needed when disposable diapers became cheaper and most parents today now use those disposable diapers.
Although some people still use the cloth diaper delivery service in LA which is the Dydee Diaper Service in LA that started in 1938.
There are some others but most places anymore do not have cloth diaper services.
Cloth Diaper services were very busy and needed and popular in the 1938 and 1940's but today disposable diapers are easier and more popular although some parents still cloth diaper their children.