But it's also interesting to think about it from the perspective of immune system compartments: the vaccine is effective in preventing severe illness and death because it's injected. But people with mild to asymptomatic cases only ever "fight it" in their mucosal immune compartment, which doesn't share antibody recipes, so people who have only received a vaccine can still spread COVID-19, because the mucosal immune compartment is not trained by the vaccine. (Hopefully, there'll be an intranasal vaccine soon.) In general, this may also be related to your general health; the stronger your immune system is overall, the less likely you're going to develop a severe infection (barring a thousand other variables) because the virus never makes it in real numbers to your bloodstream, but if you do get a severe infection the immune reaction by itself is likely to be dangerous.
At least, that's why I assume two COVID infections prior to vaccination were barely noticeable, while the vaccination itself knocked me on my ass for days and also gave me a really weird neurological episode. If I had not been required to, I would not have gotten a vaccine, since I already had a verified COVID-19 infection and recovery. So unfortunately, our policy made me pretty sick for basically zero gain, and I knew going into it there was no real upside for me (but I didn't expect the downside.)
ed: it's also worth noting that "in general" is not very useful; in this case we're talking about vaccines leveraging new technology to deliver their payload. It's not implausible to believe that the LNPs are not safe - it took several years to identify LNPs that were not obviously toxic, and it would not be wild to imagine that years down the line we find the LNPs used in the COVID-19 mRNA vaccines are unsafe in the sense that you might be 20% more likely to develop RARE_CANCER_X 15 years from now. Great article on their development here:
https://cen.acs.org/pharmaceuticals/drug-delivery/Without-li...
*: https://en.wikipedia.org/wiki/Oxford%E2%80%93AstraZeneca_COV... actually was tested: they had suspicions it caused blood clots for a few people, then they found some slightly more suspicious data. Even then, taking it was better than taking nothing for the average person – just, there were other, safer vaccines available, so nobody informed would want to take it. Its administration was halted in most countries it was approved in, once there was some evidence of harm. But the correlation's still so weak that we're not really sure it's the vaccine causing it, or even if the effect is real.
Blood clot risk is still higher if you get COVID-19 than if you get this vaccine.
In general, the worst thing an uncontaminated vaccine can give you is mild symptoms of the disease it protects you against. We are very, very, very cautious about such things (I'd argue, too cautious, but when I take my utilitarian-debate-club hat off, I am similarly paranoid, so I don't begrudge them overmuch).