But common sense establishes a causal link since in any normal year vaccine deaths (with almost half the population taking a flu vaccine) are around 150 to 200. This year they are 5479 already.
Occam's Razor certainly screams there is a casual link just from the fantastic difference that just happened to be in the year we started covid-19 vaccines. Unless you think that reports of VAERS are causing the vaccines. Or that people are just feeling a little dead after taking it from a placebo effect and their relatives thinking them actually dead reported them as being dead or other such very implausible hand waving explanation.
But the CDC is certainly able to ignore common sense and do a spin like review, and it seems they have.
I think it's a result of the Covid vaccine being new and the subject of such scrutiny.
If someone dies of a heart attack two days after getting the flu vaccine it's very unlikely to be reported to VAERS since the flu vaccine is known to be safe and no one would associate the death with the vaccination.
With Covid vaccines, on the other hand, people are hyper-aware and any health problem in reasonable proximity to the shot is much more likely to be reported to VAERS.
That's one weakness of a self reporting system - many factors influence what gets reported and there really aren't any standards.