The idea that government coercion is either morally justified or effective in achieving high vaccination rates is wrong.
I don't care to debate you about "morally justified" but you're definitely wrong about "effective in achieving high vaccination rates". It's pretty clear that states with more stringent vaccination requirements have higher vaccination rates:
"In many but not all states, philosophical exemptions are easier to get than religious exemptions, which typically require parents to cite and explain the religious doctrine in question. Overall, states with philosophical exemptions have 2.5 times the rate of opt-outs than states with only religious exemptions."