The problem with universal access in many of those countries is that it's not *quite* universal. Certainly, wherever the model is rembursment via insurance the poor have significantly worse healthcare outcomes.
The other issue is that where healthcare is operated on a for-profit basis, costs are higher with no commensurate improvement in outcomes. The extreme example being, naturally, the United States where costs are several orders of magnitude higher than the UK (eg
high drug prices) despite having significantly worse outcomes than any other OECD country.
My late aunt worked as a A&E / E.R. nurse starting in the UK and later moving to the USA. She said the difference was stark - in London the first question they asked the ambulance crews as they wheeled people through be door was "What are we dealing with?" In New York it was "Does (s)he have insurance?"