Tell me again how vaccines are the sole cause of the decline in Measles?

vital statistics measles mortality

Graph source – VITAL STATISTICS RATES IN THE UNITED STATES 1940-1960

Note the steep decline in death rates from the measles from 1900 to 1960. The measles vaccine was introduced in the USA in 1963.  – Achievements in Public Health, 1900-1999 Impact of Vaccines Universally Recommended for Children — United States, 1990-1998

Measles case fatality decreased from 21 deaths/1000 reported cases in 1911–1912 to 1 death/1000 in 1953–1962. This improvement in survival of people infected with measles virus presumably resulted from improved nutrition and medical care, especially the availability of newly discovered antibiotics to treat many of the bacterial complications of measles. – Evolution of Measles Elimination Strategies
in the United States

Was the measles considered a dangerous disease in the pre-vaccine era? 

Measles was a routine childhood ailment back in 1967, described here by the longest serving director of the CDC, David J. Sencer in Epidemiologic basis for eradication of measles in 1967 .

The clinical disease is a characteristic syndrome of notable constancy and only moderate severity. Complications are infrequent, and, with adequate medical care, fatality is rare. Susceptibility to the disease after the waning of maternal immunity is universal; immunity following recovery is solid and lifelong in duration.

Alexander Langmuir was the founder of the Epidemic Intelligence Service in the USA. In 1962 he wrote about measles in The Importance of Measles as a Health Problem

This self-limiting infection of short duration, moderate severity, and low fatality has maintained a remarkably stable biological balance over the centuries.

 The decline in mortality demonstrates the  degree to  which we have adapted to this balance and have learned to live with this parasite. Thus, in the United States measles is a disease whose importance is  not to be measured by total days disability or number of deaths, but rather by human values and by the fact that tools are becoming available which promise effective control and early eradication.

To those who ask me, “Why do you wish to  eradicate  measles?,”  I  reply with the same answer that Hillary used when asked why he wished to climb Mt. Everest.  He said, “Because it is there.” To this may be added, “and it can be done.

Decline in Measles death case ratio began in 1930’s.

The annual number of measles deaths in the United States fluctuated between 2000 and 10,000, and the death-to-case ratio (DCR; the number of reported  deaths  per  1000  reported  cases)  generally ex-ceeded  10  (figure  1).  The  number  of  deaths  and the DCR began to decline significantly in the 1930s, most probably as a result of treatments for secondary infections   [1–4],   improved   nutrition   [5],   and   reduced crowding [6].

Acute Measles Mortality in the United States, 1987–2002

(All emphasis throughout is mine)