I don't think it's unreasonable to temporarily halt vaccinations if there is suddenly a new side effect.
If you tested the vaccines on 1 000 000 randomly-sampled individuals and only ten of them died, that doesn't mean the probability of dying is 1 in 100 000. The outcome doesn't always depend on just the vaccine, but also the person: their health, their genetics, etc.
Even if you sampled 1 000 000 people from the entire planet in a truly random fashion, you can expect about 130 people to be from a specific population of size 1 000 000 (hypergeometric distribution). If even a single one of them dies and the cause is due to a characteristic unique to this population e.g. isolated genetic history that creates a "common" genetic condition that leads to a lethal immune response, that's suddenly 1 in 130 chance of death for that population.
Take Finland, population ~5.5 million. Expected number of Finns among the global 1 000 000 tests? About 700. If one of them dies due to a vaccine interaction with a condition abnormally prevalent among Finns (e.g. a Finnish heritage disease), that's 1 in 700. Or an expected number of deaths of about 8 000, far from the 5-6 people that you would expect with a 1 ppm probability of death.
Now obviously, not every Finn would be at risk of death since not every Finn has a Finnish heritage disease (~20 % has as at least one related gene defect). But it's important to rule out the possibility, or you'll end up with another Pandemrix narcolepsy PR fiasco that leads to more vaccine hesitation and skepticism.