Hygiene played a very important part in health. It was what turned cities from population sinks to population sources. It only goes so far.
The effectiveness of vaccination has been demonstrated numerous times, both from epidemiological studies and just looking at who's been vaccinated and who gets something. Smallpox was eliminated by vaccination performed all over the world, in areas with wildly varying social, hygienic, medical, environmental, and nutritional conditions. Polio is either eliminated or confined to one small area in the world; I haven't been keeping track. Very simply, there's all sorts of evidence that vaccines work.
Dr. Wakefield published a fraudulent paper linking autism to vaccinations, apparently to try to sell his thimerosal-free vaccines (thimerosal is not present any more in first-world vaccines, although it's necessary because of bad transportation and storage conditions in less developed areas). The paper was examined and found to base its conclusions on lies. Since then, there's been a lot of study on vaccinations and autism, finding no link.
I don't know why delaying the measles part would be a bad idea, but I bet the CDC could tell you, except that you don't appear to believe in scientific conclusions. Last time I wondered about a certain vaccination, I found the CDC site had reasons for the recommendation.
An experiment with the MMR vaccine such as you suggest would be highly unethical, and would land the experimenters in a great deal of legal trouble, because it would involve arbitrarily depriving children of safe and very beneficial treatment. Double-blind experiments cannot always be carried out on humans, so we have to study some things in more roundabout ways.