This particular article is.. just trying to drum up why people shouldn't get the vaccine. Without saying, "don't get the vaccine."
Should people get natural immunity? No, what a daft idea when a safe vaccine exists.
You wouldn't say the same about smallpox. Good lord.
There is only "immunity", which you gain after recovering from Covid. Whether you were unvaccinated or vaccinated at the time of infection is something that affects the risk of serious illness. But once the person has recovered, they are immune and need no further vaccines or boosters, since they have nasal immunity, serum/blood antibodies (for a period of time) and long term T-cell defenses.
A vaccinated and Covid-naive person is not immune, they are only protected from serious illness. The CDC updated their website in Sept. 2021 to make this clear.
Hospitals should prioritize hiring of nurses, doctors and other personnel with immunity.