UK health care workers were one of the main groups affected by Pandemrix-related narcolepsy. It was a bit of a scandal over here, though perhaps not the most well-known one.
The "issue" I've heard with simply referencing fatality rates is that the fatality rate does not equally apply to all age groups/risk factors.
So anyone under 30 has a dramatically lower chance of dying due to covid, and therefore would likely have a higher risk of a serious side effect when compared to the risks of contracting covid.
It's an interesting dilemma, for the good of public health you have to have certain populations actually increase their own personal risk, at the benefit of the majority overall.