About everyone will get it sooner or later, vaccinated or not. (Pets are a reservoir, and nobody is vaccinating them.)

The best to hope for is not to die, be hospitalized, or suffer various long-term or permanent effects. Vaccination is all we have to prevent those.

Yes, but measures like the policies in question encourage people to get infected with symptomatic COVID so that they could go to doctor and get that very useful piece of paper.

That's the point. If you wanted to ensure people to not get COVID, do not give those who have had COVID pleasant exemptions. They failed, they should not be rewarded.

If everyone will get it, then no one who gets it and does not die or become seriously inconvenienced has failed. Dying, of course, is usually a fail, but literally everyone will do that, too.