> New influenza vaccines (using cell lines) were approved after use in 15,000 people
The are several important differences: (1) it took 4 years of data, not 6 months of data like Pfizer, (2) using mature, well known technology.
Now, let's compare to a flu vaccine approved with an EUA after 6 months, shall we?
https://www.bmj.com/content/362/bmj.k3948
https://www.sciencemag.org/news/2015/07/why-pandemic-flu-sho...
(Both articles describe the same vaccine, pandemrix)
It caused narcolepsy, a few hundred cases of it. That's a debilitating, life changing disease; by all estimates I know, much worse than the flu it was supposed to prevent. It's not the only case (though there aren't maney - 1976 flu vaccine causing guillan-barre, dengvax worsening dengue, israeli anthrax vaccine causing harm, probably a couple more I'm unaware of; the vast majority of vaccines -- all that I'm aware of that got full approval rather than an EUA - have a 1:1,000,000 or better adverse event profile).
And it isn't even perfectly clear why. The science article says it's likely because there's a similarity between some viral protein and some brain protein -- but that's not clear that's the reason. According to the BMJ article, basically the same vaccine but with a different adjuvant caused none of the issues.
How long did it take to figure this out? Approximately one year of data.
I urge you to read the BMJ article - it eerily describes exactly what's happening now, 11 years ago - some of the names (e.g. Fauci) haven't changed; some have.
> Are you overestimating the safety testing done on other vaccines?
I don't think I am. That's why we have VAERS and a European equivalent. You might notice that a lot of the touted efficiency and safety data is coming from Israel. Well, Israel has no VAERS equivalent, hardly tracks any adverse events for this vaccine (likely on purpose), and decreed that vaccinated people are not to be PCR tested unless they show obvious COVID symptoms, whereas unvaccinated are required to have negative test from the last 48 hours for many activities -- which means the data will show it's working even if it doesn't. Israeli data is rubbish, other data is hardly available. (I currently live in Israel and track this; It's been politicised in Israel to the point that no data coming out of Israel is trustworthy)
So, regardless of safety of other vaccines, we have very little reliable data about the new guys.
> but I wonder how you've gone about assessing previous safety proofs.
By waiting enough time to get data accumulated.
You know why we ddin't have any corona virus vaccine before 2020? It's not for lack of trying. They all failed at various stages, all of which were skipped for the SARS-Cov-2 vaccines.