Noted also that private healthcare insurance does exist in Denmark ..
I think that's true in every country. Health care is complicated but I don't see any other country in the world giving up their system in favor of our totally dysfunctional one. And I'm pretty sure no other country allows for private insurance to be a for profit enterprise. Compare that to ours where the UnitedHealth CEO's pay passed $18 million in 2018; Optum chief got $21 million in his first year https://www.bizjournals.com/twincities/news/2019/04/22/unitedhealth-ceos-pay-passed-18-million-in-2018.html
Healthcare costs
Public healthcare funding In 2016, the Danish healthcare expenditure amounted to $5,205 U.S. dollars per capita (approximately 10.4 percent of GDP), with around 84.0 percent of healthcare expenditure being funded by governmental or compulsory means.[7] Healthcare in Denmark is largely financed through local (regional and municipal) taxation with integrated funding and provision of health care at the regional level. The national tax for healthcare is set at around eight percent of the total taxable income.[8] The money is then disbursed to be used by the five administrative regions of local government according to the guidelines set by the central government.
Private healthcare funding According to the OECD, in 2016 the private healthcare expenditure in Denmark was $831 U.S. dollars per capita (approximately 1.7 percent of GPD).[7] The private healthcare insurance aids in covering a variety of copayments not fully covered by public healthcare funding.[8] https://en.wikipedia.org/wiki/Healthcare_in_Denmark