Correct me if I'm wrong -- I thought current (mandatory) vaccines have been quite thoroughly tested?
The idea people have that vaccines are perfectly safe is incorrect - it's more of a case of some doctor deciding that it's worth the risk, of the 'benefits outweighing the risk' -.
Vaccines change the way your immune system responds to its environment and it's hard to know the long term effects exactly.
Furthermore, there are no guarantee people will catch a given illness, and in the case of the vaccine, it is purposefully administered rather than more of a happenstance.
Yes, overall vaccines are 'very safe' but if they find a vaccine for an ongoing pandemic they're going to greenlight it far more easily due to exceptional measures. In all likelihood, governments would be happy to preemptively exonerate whatever pharma company produced said vaccine of any responsibility for the occasional death if it meant a quick resolution to the situation. And of course, the same people who greenlighted it would not have any interest to check the aftereffects with too much zeal.
And even with very low numbers, you can find paradoxical situations where a disease is eradicated but still vaccinated against and where the illness causes 0 deaths but the vaccine will kill a few people per year. So as I said it's a doctor saying 'it's worth the risk' - rather than the magical shield gov PR says it is.
edit:
To give some examples :
+ in 1955 a vaccine against Polio gave 40,000 people Polio (including 51 paralysis and 5 deaths),
+ in the 70ies an influenza mass vaccination campaign saw 10,000,000 people vaccinated and caused important medical issues for 1,000 people, including 53 deaths. It was for an epidemic that finally never came out of its initial foothold in the US (a military base)
+ the Yellow fever vaccine can in rare cases (approx 1 in 300,000) cause multisystem organ failure and death.
+ The yellow fever vaccine can also create inflammation of the brain at a rate of 1 in 100,000 - while rarely fatal if treated i'd assume it can cause brain damage.
+ smallpox vaccine kill approx 1 person per million doses administrated, additionally it can kill fetuses if injected in pregnant women.
+ etc.