There are some sizeable demographics for whom this may not be the case: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4125239

> The excess risk of serious adverse events of special interest surpassed the risk reduction for COVID-19 hospitalization relative to the placebo group in both Pfizer and Moderna trials (2.3 and 6.4 per 10,000 participants, respectively).