Firstly, the claims aren't extraordinary. There is a long history of vaccines being suspended for being more dangerous than is worth it, for example here's a CNN archival story about that:
https://edition.cnn.com/2009/HEALTH/04/30/swine.flu.1976/ind...
"ATLANTA, Georgia (CNN) -- The man who led the response to the 1976 swine flu outbreak is defending the vaccination campaign that led to more deaths than the disease, but says he's sorry for the people killed or sickened ... the program was suspended after at least 25 people died from vaccine reactions"
In 2010 there was another Swine Flu scare but not much was learned: Pandemrix was authorized and sold in Europe but turned out to occasionally create narcolepsy in teenagers. Although rare, swine flu was sufficiently mild that this was much worse for the affected people than actually getting the disease would have been. There was a coverup and the true nature of what happened only came out 5 years later thanks to lawsuits.
So there's nothing odd about the idea that a vaccine may yield more injuries or deaths than it can save. It's happened before.
Now, I've already cited the evidence you require: the data from national vaccine reporting systems. That's the graph at the top of the page I linked. You appear to have simply ignored the graph and then gone off on some other link to a paper you found there, which isn't what I was referring to, and at any rate seems to actually support my point. Multiply the Y axis of the graph by 0.85 if you want - the numbers are still radically higher than the normal expected rate of vaccine side effects. Or don't. But actual government data cannot be handwaved away with an argument of the form, "some random paper looking at the data has some limitations that it openly admits to" because I wasn't basing my point on that paper to begin with.