I think your stance on poverty (and how to get out of it) is wrong on a fundamental level, SD Nihil.
You stated repeatedly that hard work and effort will always enable you to beat poverty. But that's only one factor, out of many. You have to consider all of those. Surely you agree that chance, luck and circumstances are important as well? What about talent and intelligence? Either you're born with those traits or you're not. They affect your success, just like effort does.
Long story short, some people will not be able to afford healthcare, no matter how hard they try.