This Danish study (https://www.medrxiv.org/content/10.1101/2021.12.27.21268278v1.full.pdf https://www.medrxiv.org/content/10.1101/2021.12.27.21268278v...) of Om

This Danish study (https://www.medrxiv.org/content/10.1101/2021.12.27.21268278v1.full.pdf https://www.medrxiv.org/content/10.1101/2021.12.27.21268278v...) of Omicron household secondary attack rates found a 52% reduction in susceptibility for boosted individuals and a 51% reduction in transmissibility from boosted individuals. In other words, if both the infected person and the household member were boosted, the likelihood of a household member becoming infected was reduced by 74% compared to if both were unvaccinated. (This number is for Omicron, for Delta the reduction is even higher at 92%.) In other words, while you are technically correct that the vaccines do not completely prevent infection or transmission, they do, in fact, significantly reduce the likelihood.