Certainly, sanitization and antibiotics played a large role in reducing death rates from these diseases. But death rates are misleading here. Disease incidence is the relevant parameter to assess the efficacy of a vaccine, and that only under the assumption that vaccination rates of 80-90% in the relevant nation are achieved.
Great that most of these graphs have the vaccine introduction far on the right of the x-axis )whooping cough, diphteria, measles) or the covered timeframe is negligible (polio) to the time that is needed for the vaccine to take effect in the whole population.