Were the reduction hostpital admissions and deaths purely (or even mainly) due to the vaccines, though? Or was it also because many vulnerable people died early on and because the virus got weaker over time? Without tight controls, correlation doesn't prove causation. There are so many variables at play here. For example, perhaps a lot of the people who got vaccinated were health and hygiene conscious in other ways too, such as thorough hand washing, social distancing, good nutrition. Perhaps many unvaccinated people were people who didn't care and were not being sensible in other ways. I'm speculating here, but just highlighting the difficulty with saying that result B is definitely due to cause A.

And that's before we even come onto things like the possibility of the PCR tests being innacurate, and the difference between dying WITH the virus and dying BECAUSE of it.