I get your premise and it's true for a lot of stuff, but the equivalent is saying that following the rules of the road white driving is a personal choice. When choices start effecting those around you it's a different animal.
When one drives recklessly, we know the result, bodily harm to themselves and or others. When one takes a new vaccine with limited testing and emergency approval, we don't know the result(s), yet.
By that logic, every set of choices one could have that affects others should be regulated or overseen?
Moreover, that comparison is predicated on the belief that vaccines prevent transmission. There has been no sufficient data (to my knowledge) that backs up the claim of them doing so.