You forgot to mention that not all diseases vaccinated against are easily communicable. Polio for example is spread through fecal matter and contaminated water. You're not going to get it if you touch someone with polio and it isn't airborne. Hepatitis is an STD, what are we doing giving that to children that are unlikely to be exposed to it until they are older? What your toddler is going to be hanging out at the strip club or doing drugs?

Frankly I find the whole question of community welfare is utterly moot. One is not obligated to determine their health decisions based on their impact on the community. It comes down to health freedom. Whether you believe in vaccines or not one should be free to get them or not. Making any medical procedure mandatory is a gross violation of medical ethics.