The captive audience problem is the core of much of the vaccination program.
Hep B - given to babies because the problem population is "hard to reach."
Hep A - young children are usually asymptomatic or very mildly sick -- they're vaccinated so that they don't spread Hep A to adults.
Rubella- mild illness, no risk to children - we again vaccinate children to protect pregnant women.
Influenza - a key component of the newish national immunization strategy is that schoolchildren (who are generally at very low risk of complications from flu) are the ones who "spread" the flu to the elderly. So, we vaccinate kids to "protect" their grandparents.
Kids are powerless and helpless -- they are not capable of refusing the shots, and their parents can be easily scared and bullied into consenting.
Vaccinating babies as young as possible solves another major issue -- it's much easier to downplay a frightening side-effect if it happens in a person who is unable to explain what is going on with their body. I almost threw up when I read the info sheets about the vaccins listing "crankiness" as a possible "minor" side effect. Hello! Cranky is not a diagnosis. Cranky is a symptom of something being WRONG. If it was somebody old enough, they'd be able to tell you that their head felt like it was going to explode, or that their neck was feeling weak, or that their vision was blurry, or they felt like they were going to throw up, or that they couldn't move their leg without blnding pain. But if that person is two months old, you can write it off as "cranky." And then, everyone can laugh and smile knowingly, and say that "he's just cranky because he got shots today."
Besides, if you're two months old, and you die the next day, somebody can call it SIDS.