You forgot the 25% sales tax in Denmark from your calculations (sales tax a very regressive form of taxation). In the usa the average sales tax is 6%. What you are saying in essence is that the US should significantly increase taxes and then give people these services? so lets put this into better perspective:
A middle class family in the USA (most middle class have some form of health insurance and are paying lets say 400/month employee contribution) vs Denmark for comparison.
Net income of 66k USD (50k Euro) in the usa they will spend about 3k/month on taxable items (50% is housing related the rest is spent
... who saves anymore?). that means in the usa
3000 * 6% = 180
3000 * 25% = 750
so you see you are paying significantly more for your health coverage then the average person in the USA
that 180 in sales tax in the USA is also going to subsides University, you can not compare the price of a private college to a state university for in state residents. The cost of instate is 8000/year * 4 years = 32000
Lets divide that number over a lifetime say 60 years of paying sales tax will be 45 dollars per month.
So now lets add 180 + 400 + 45 = 625 vs the 750 you are paying
... overall USA is less expensive the major difference is not in quality of care but in compensation when things do not go according to plan. The reason the USA doesn't have universal health care is quite simple
... malpractice to sum up the situation:
Democrats make their money as trial lawyers and many of them made their fortunes on malpractice issues so a federal health care system would also mean no more malpractice claims in the 10s of millions of dollars but more in line with Denmark system:
Republicans do not want a federal system they want it controlled by the state
... and thus set by insurance companies (that charge significant amount for that malpractice insurance) that they will lobby for when they leave office.
so in short both Democrats in the USA and Republicans in the USA agree that Universal healthcare is bad for their pockets