There have been > 111k breakthrough infections in the US alone through the end of July. The CDC stopped tracking them unless they resulted in hospitalization or death, but we can still look at the data from the 35 states still tracking it.

It is fair to say that vaccination reduces the chance of infection. "Very rare", however, is not how I would characterize it.

https://www.bloomberg.com/news/articles/2021-07-30/cdc-scale...

Data from Israel suggests that efficacy may be much lower than initially believed, but still much better than nothing.

https://www.sciencemag.org/news/2021/08/grim-warning-israel-...