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Lack of statistical significance does not mean you get to assume the outcome you want, it means you can't say for sure if the effect exists or not. Therefore if you see more people who take the vaccine die than those who didn't, you need more data. End of story.

This should be obvious, indeed, obvious from high school statistics classes. If the effect does in fact exist and you roll out the vaccine on a global scale, you will end up creating a truly enormous number of deaths that should have never happened. Therefore you must be sure that the number of deaths will reduce. Their data couldn't prove this so it should never have been approved. But of course the whole thing was on rails from the start. The idea that governments would have rejected the vaccine trials when they were telling people vaccines were the only way out of lockdowns and buying up millions of doses before the trials even completed, is naive in the extreme.

The core problem for COVID vaccines is of course that COVID just isn't very deadly and many of the so-called COVID deaths were in people dying anyway of other reasons where the cause of death was spuriously mis-assigned, i.e. not people who will join trials. That's why they struggled to show any impact on death.