They do. If you have a "breakthrough infection", you are just as likely to spread it to someone else as someone who is infected without the vaccine. But you're

They do. If you have a "breakthrough infection", you are just as likely to spread it to someone else as someone who is infected without the vaccine. But you're much less likely to get infected in the first place if you've had the vaccine, so overall much less likely to pass it to others. So the more people who get vaccinated, the slower the spread. See https://covid.cdc.gov/covid-data-tracker/ https://covid.cdc.gov/covid-data-tracker/