That intuitively doesn't make sense for the fact that vaccines help produce antibodies which prevent the virus from spreading within the body and reproducing within the body. The spike protein is detected as something bad, and the body becomes furious and destroys the whole shebang, but not before binding to the spike protein as well and preventing it from infecting cells. If there's a lower viral load in the body, then it reduces the chance of spread (hint, because viral shedding is what causes spread across people).

Put away your exclamation points and have a glance at https://www.nytimes.com/interactive/2020/health/pfizer-biont...