I don’t get your metaphor at all. This isn’t about assumptions.
Is there a case to be made that requiring vaccination against X is legal?
Perhaps, but that follows from specific circumstances regarding X and the duration.
Any new vaccination against Y requirement must be argued from that, not merely because we already vaccinate against X. the only thing we can take as a given is that a vaccination mandate for Y is possible, because a vaccination mandate is possible.
And that’s not even taking in account that different cultures and legal traditions will value certain things above others.
My country’s constitution, for example, has far less free speech protections as that if the USA, but a high a high emphasis on “human dignity”, which inconveniently makes mandatory vaccination a hard thing to implement.