Would you take the anti-vaxxer pledge not to go to hospital?, page-454

"So in saying that , getting vaccinated cant lessen the chance of transmission, from the early days of covid.
What is the govt trying to achieve, I thought lessening the spread. A working vaccine should lessen the spread."

it does lessen the spread
you are focussing on what happens when a breakthrough infection occurs.
The fact is less vaccinated people get covid, so it does lessen the spread.

"By July 25, 2021, a total of 10,175,425 (65.8%) New York adults aged ≥18 years were fully vaccinated; 1,603,939 (10.4%) were partially vaccinated. Among fully vaccinated adults, 51.3% had received Pfizer-BioNTech, 39.8% had received Moderna, and 8.9% had received Janssen (Johnson & Johnson) vaccines. During May 3–July 25, a total of 9,675 new cases (1.31 per 100,000 person-days) occurred among fully vaccinated adults, compared with 38,505 (10.69 per 100,000 person-days) among unvaccinated adults"

https://www.cdc.gov/mmwr/volumes/70/wr/mm7034e1.htm

"This study’s findings suggest currently available vaccines have high effectiveness for preventing laboratory-confirmed SARS-CoV-2 infection and COVID-19 hospitalization. However, VE against infection appears to have declined in recent months in New York,"

So if the chances of getting infected are lower if vaccinated, the chances of spread is lower.