Quite right. And furthermore, if 99% of the population is vaxxed, and the vaccine only cuts the incidence of serious illness by (say) a factor of 10, then 90.

Quite right. And furthermore, if 99% of the population is vaxxed, and the vaccine only cuts the incidence of serious illness by (say) a factor of 10, then 90.8% of the seriously ill patients will be vaxxed. And in that case, calling it a "pandemic of the unvaccinated" and concentrating your efforts on trying to force the last 1% of the population to get vaxxed will not help much in reducing the load on hospitals.