It's about the unknown - the possible rare long-term AEs that may appear later on. If I am making a decision about risk-benefit I want to know as much as possible about my risks and my benefits. My risk of serious disease with COVID is very, very low and my risk of contracting COVID is very low as well, so if I were to take the vaccine, it better have minimal AEs.
A good example is back ten years ago, there were several vaccines rushed for swine flu. Most were good, but one - not used in the US but in the UK and some European markets - caused rare instances of narcolepsy with cataplexy. None of the other vaccines did. Things like that...