Poor people can't save
the person would have no problem paying for the health care if it was charged in the form of taxation over time instead of all being charged in 1 lump when they get sick.
Isn't this a bit of a contradiction?
No. The advantage of taxation is that there is no way that the normal emergencies of life can eat into the fund needed for health care. The vast majority of people cannot save up a sum of £10,000 yet that is the bare minimum they will need for end of life care.
http://www.newyorker.com/talk/financial/2012/01/02/120102ta_talk_surowiecki?currentPage=allHere is an example of the same thing...people are using the most expensive possible way to finance consumer purchases because they cannot save the money themselves.