Omicron is starting to change that statistic. In Australia, for example, the total hospitalizations for the month of December between the vaccinated and unvaccinated are nearly on par. Move unvaccinated went to the ICU and more vaccinated died (12 vaccinated vs 10 unvaccinated).
The prominent graphs are all pandemic-wide totals. You'll want to scroll all the way at the bottom, look at the raw data.
It's a MSM/DNC myth that this is only a plague of the unvaccinated, especially as we get more and more variants. Admittedly, when you control for the fact that the unvaccinated are ~25% of the total population, we're still statistically overrepresented. I think you're correct in your assertion that we haven't achieved total global viral saturation quite yet. When that happens, we'll definitively see whether natural immunity or vaccination is more effective at maintaining long-term immunity in the hospitalization rates.
BTW, Australia's own vaccination #'s contradict your theory. Where did you hear that 95% of your population was vaccinated?