I see your points, but not necessarily the logic.

Instead of being the government the one setting the limits to what is 'national health', you are saying that it should be private companies. So when the poor old man is denied a feeding tube by a private company (on the same cost/coverage rationale) things will be better? Nonesense...

Minimum wages are not (only) about 'lifting the poor out of poverty', its objective are many and is not free. Something to consider: a) ensure a minimum standard of living (ie: food, clothing, etc). and b) avoid exploitation by ruthless companies. With (a) you try to tackle many issues (crime, education, health) at its roots. And (b) is to avoid economic 'slavery'. I'm not saying that it works perfectly, just what the intended investment is, and how you have to measure its performance. There are other (possibly) concurrent measures to include in the analysis. Minimum wages should not be dissected in a vacuum...

True, capitalism is a great generator (and accumulator) of wealth. But one of the worst systems at distribution. You know the old saying "the rich are getting richer, while the poor, poorer"... it's not just a propaganda slogan. The patterns of income and wealth accumulation are there for anybody, honest enough, to see. Go look it up http://www.census.gov/prod/www/abs/poverty.html
BTW, it's not just poor vs. rich. The issue also includes the percentage of wealth that each segment of society has. A relatively good executive summary: http://www.epinet.org/books/swa2004/news/swafacts_international.pdf