No, it won't be almost zero because they're including health insurance premiums in that figure. Few jobs in the US cover 100% of the premiums for their employees.
>> The cost of health care is composed of two subcategories: (1) premiums associated with employer-sponsored health insurance plans and (2) out-of-pocket expenses for medical services, drugs, and medical supplies.
Because preferences for food, housing, and healthcare are essentially unbounded, I think you will always have unmet preferences.
It must be more nuanced than you say, as millions of people reach old age without sharing your concern.