On the side of legally mandated vaccines, lots of countries mandate vaccines without religious or personal exemptions. Only health based contra-indications can be used an excuse to not have them (for kids/mothers).
Other countries even have legal requirements of vaccination to work in certain high risk professions (health/child/communal/elderly care) or travel (eg: meningococcal for Hajj)
Having a govt which makes only good decisions is not just important for vaccines but also other parts of life. Your doubt of seatbelt having no downside is not completely correct. It has a well-documented and unaddressed substandard to negative impact on people with non-standard size/weight/shape.
Your doubt is what make me think this vaccine hesitancy is deeply social, not just personal. It is not seen in several societies