The current situation in Auckland, New Zealand provides very good evidence of vaccines reducing spread, though I don't think it has been written up in a paper yet.
We've had < 10,000 confirmed COVID cases in Auckland so the vast majority of the 2M population cannot have natural immunity. Behavior restrictions have been relaxed gradually over the last two months, yet the COVID case numbers (which were increasing) have actually leveled out at an R value of around 1. Vaccination is the only thing that could plausibly have reduced that infection rate.
We've had < 10,000 confirmed COVID cases in Auckland so the vast majority of the 2M population cannot have natural immunity. Behavior restrictions have been relaxed gradually over the last two months, yet the COVID case numbers (which were increasing) have actually leveled out at an R value of around 1. Vaccination is the only thing that could plausibly have reduced that infection rate.