This is not correct.
As an example, have you had the smallpox vaccine? It is effective for about 10 years before the effectiveness reduces, so a top up is needed.
The anthrax vaccine? It needs 3 or 4 doses and regular top ups, and it only gives resistance.
The tetanus vaccine? It lasts about 10 years also.
Lots if vaccines have a time period where they grant primarily resistance. In the case of something like anthrax, the objective is to make it largely survivable.
I know you used a lot of your logic to arrive where tou are, so hopefully this additional information allows you to arrive at a better conclusion.