For one, I am not sure about the side-effect-freeness. In fact, the covid vaccine is the first vaccine I know where a high percentage of people I know who have got the shot also were ill for a few days. So this is new for me. I have got a lot of vaccines around 15 years ago for a travel gig, and didn't have side-effects from a single one of them. So this is new, me having to accept that the vaccine might take me out for a few days.
And yes, of course, with a different situation, my decision might be different. If covid were as harsh as our media and government claimed at the beginning of the first lockdown, I would certainly get a shot. However, it turned out the media and government have overstated the danger, apparently to achieve compliance. This sort of lie (we were told "everyone will know someone who died") was my wakeup call. I was originally mislead and expected a deathrate of 1%. As it turns out, almost only the elderly die, and the deathrate (including the elderly) is around 0.1%. Wrong order of magnitude for real panic on my side.