The vaccines are somewhere between 60-95% effective, several weeks after the second dose. Most vaccinated people are not that far past the second dose, or are only on their first.
At the point when virus levels are low in the community, 90% effectiveness from a vaccine means most of the 10% who do not respond never encounter anyone with the virus, when virus levels are high there is a much bigger chance that 10% will meet someone infectious and become ill.
Herd immunity from vaccination only works when enough people are immune to stop onward spread, because no vaccination is 100% effective and no population has 100% vaccine take up.
Eradication of viruses by vaccination is possible (smallpox), but it takes years of vaccinating most of the population worldwide and concentrated efforts to vaccinate around any clusters.
Measles was almost eradicated in this country, but as it's still endemic in other parts of the world, we have occasional outbreaks because some vaccinated people are not immune and other people are not vaccinated, so there are enough susceptible people for some spread.
The vast majority of the population are not immune to covid, so as soon as anyone abandons social distancing it risks spread between the majority of the population, who are unvaccinated, and the unlucky few for whom the vaccine doesn't work.