Everybody in the US has insurance, that was literally a major point of contention to Obamacare - the left didn't like that the solution still used private insurers and the right didn't like that they were forced to buy something. If you have a low income, you get subsidized premiums.
For sick pay, it's just a lack of budgeting and planning. If you have a job that pays you $12/hr with no paid leave time or a job that pays you $10/hr with an accumulation of leave hours, it's still the same in the end if you work X days and are sick Y days and get a monthly income of $ZZZ, just in one case your employer is holding back your leave pay and in the other case you're paid full value up front and save for your leave period yourself.