What is not science?
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I both cases are the number of events "." the same number. Let "x" be a problem then we see in the second case here the problem "x" 10 times faster. => The more people are vaccinated the less plausible is what you say.
And in general seem to be your "hypothese" a self-fulfilling "hypothese". If no one makes a vaccination because a vaccination seems to be dangerous then no one will find out that it is not dangerous.
There is no substitute. Body chemistry, immune system reactions can't be sped up or slowed down to accommodate an outcome. This isn't a physics problem.