They do prevent infection - not as effectively against the later variants but still notably - and the side effects which the right-wing media is stoking are indeed more common and more severe from an unvaccinated case of COVID than getting vaccinated:
https://newsroom.heart.org/news/myocarditis-risk-significant...
It's so odd that Israel found no significant increased risk of myocarditis from SARS-CoV-2 infection in a very large study conducted before vaccines were in widespread use: https://pubmed.ncbi.nlm.nih.gov/35456309/
Since the risk of COVID varies wildly by demographics, this leaves open the possibility that the vaccines are a poor risk/reward tradeoff for large numbers of the people it's being recommended to (essentially, everyone over 6 months old). And since they don't prevent COVID infection, "risk of vaccination" vs "risk of a COVID infection" is the wrong comparison to make in the first place.