Everything around epidemiology is an estimate, and outcomes have to be measured at the population level due to variance between individuals, which is why anecdotes never qualify as data. You can certainly compare populations who have been vaxxed vs those how have not to build mortality and morbidity models. The issues is the completeness of the variables around each member of both groups, which is the core data collection issue of any population level medical study around humans.

This is easier to do and more reliable than you are indicating when done at the population level. Yes, I have done vaccine efficacy research in the past when I doing systems work in vaccine registries. I have built statistical models and still do. My last gig before my current job was building algorithms around pathogen detection.