The problem is, nobody appears to be actually, aggressively researching to what extent there is a causative relationship between the vaccines and reported adverse events.

That's the crux of it. It's the same with the MAERS reporting system in the US. The authorities say 'Oh, it can't be trusted coz of this and that reason' - but where the hell is the reporting system for adverse events that can be trusted? It's buried in a 3-month 'investigation' process conducted by pro-vaxxers that somehow never ends up seeing the light of day.

Those 'Fact Checking' sites really get on my goat. Here's an example of the sort of propaganda they were pushing:

PolitiFact, for example, on May 24 quietly retracted a September 2020 fact check that labeled a Hong Kong virologist’s claim that COVID-19 originated in a lab as a “debunked conspiracy theory.”

"The claim is inaccurate and ridiculous. We rate it Pants on Fire!”