That's what health insurance is for. If this was being driven by some sort of rationality, health insurers would just (be allowed to) increase premiums for people who don't take the vaccine. That would force people to properly calculate the true staffing needs imposed by them and pass the costs on to the right people.

This type of mandate does the opposite. Probably because, if you look at the actual risks and data from other countries, the difference in sickliness between the vaccinated and unvaccinated is sufficiently small in absolute terms, and the level of staffing at hospitals assuming healthcare workers are not forced out of their jobs sufficiently good, that the relative cost increase wouldn't work as a form of coercion. And it's now all about the coercion, not about health.