Lockdowns give you a linear factor to flatten the rise of new cases that is relevant even for an exponential curve.

Some said that vaccination proved a 70% protection to infect someone. Makes sense since the time someone can infect others is shortened because of the quicker immune response. I still believe this to be a noble lie however, since we should have seen an effect, but the curves rose just as quickly in vaccinated/unvaccinated countries and as fast as in the first wave.