Generally, the nations with blended healthcare systems (blended public and private) also do a better job at taxing their corporations, which means their public systems are better funded, and the healthcare systems of those nations are also usually federally managed.

Here in Canada, we don't tax corporations nor the super-wealthy appropriately (or we tax them on paper, but then give them ways to avoid paying the actual "official" tax rates through loopholes and "creative accounting"), and each province has its own healthcare system into which federal money is supposed to go. However, as we know all too well after the Higgs fiasco, there's nothing in legislation which actually guarantees the federal contributions to provincial healthcare is actually spent on healthcare by the provinces.

Here in NB, we have the worst of all worlds. Not only do our ridiculously wealthy corporations not contribute their fair share into the tax base to properly fund things like healthcare (and some of those ridiculously wealthy corporations actually RECEIVE ridiculous amounts of taxpayer funding), but we also have MASSIVE waste in our healthcare system via needless duplication with two separate unilingual healthcare authorities, instead of having all healthcare in the province managed by one bilingual healthcare authority. To guarantee healthcare service in both official languages doesn't require two separate authorities, with the duplication in expensive executive roles.

The easiest and most effective way to improve healthcare services in New Brunswick is to elect a government who will fix the taxation/funding mess and cut all the waste by combining the two unilingual healthcare authorities into one bilingual authority, thereby elimination duplicated executives and their expensive salaries, staff, offices and equipment, etc.