The mandated vaccines are those that are generally accepted by the medical experts, and with historical evidence, as being safe and effective against severe childhood and adult diseases, which are highly contagious.
The purpose of everybody hopefully being vaccinated at pre-school age is to prevent contagion in the close quarters of schools
Another purpose is to hopefully eradicate these diseases by creating "herd immunity". For example, measles and polio were thought to be eradicated, but due to laxity in people having their children vaccinated, those diseases have reappeared.
Nobody is mandated to take the pneumonia or the shingles vaccine, and many other vaccines such as those that are available for certain types of Hepatitis. That is their personal call and probably on the advice of their physician.
But when it comes to the generally mandated vaccines, I can't agree that recommendation should be left up to individual physicians with their own possibly misguided and/or misinformed theories and opinions.