Good points. Indeed there are other points, besides the fact that we expect hospitals to continue to function as they are without any changes to the society which is making people sick.
First you mentioned poverty, which is a big Part of what makes people sick. Creates downstream consequences which sends people to the hospitals. Much cheaper to deal with the issue first rather than pay for care later.
Also much cheaper to make sure prenatal and natal care up to the first 5 years (to include parental leave, paid) makes sense as preventing bad health will help us a lot later on.
Also inequality makes the entire society sicker.
Until we realize this we will continue to dump on the health care system continue to pay more while our mortality rate worsens.