It also does NOT establish universal health CARE, it establishes universal health INSURANCE.
It's amazing how some people don't get that any deal, including provision of medical care, has two sides, a buyer and a supplier.
Health care is the supply.
Health insurance is (an organisation of) buyers.
By providing health insurance to all, the supply is not directly affected. Universal health insurance does not imply universal health care.
What universal health insurance will do is lower prices. Universal health insurance pools buyers and creates a monopsony. Monopsony power forces prices down.
But the lower the proces the fewer people will want to supply (and the worse the quality of the supply becomes).
Draginol once explained that there is only a finite amount of healthcare to go around, just like with any product (i.e. there is no infinite amoung of cars, which is why cars cost money). Currently that finite amount is channeled into the market according to how much every buyer is willing to pay.
Universal health insurance will bring down prices.
But it will not change the basic fact that halthcare is not an infinite resource and the fact that it lowers prices will actually make decrease the amoung of healthcare available in the market (since, for example, fewer people will want to work as doctors if the pay goes down).
Assuming a model society with 10 people (with 10 different incomes) and 3 doctors (who will provide for 3 patients each), the current system will cover 9 of the 10 people and the best of the three doctors will have the richest 3 patients.
If universal health insurance somehow managed to give all 10 patients the money to pay for their service, the 3 doctors will still only be able to cover 9 people (since their number has not increased) but there might not be 3 doctors any more since the healthcare costs went down and maybe one of the 3 finds he can work in another country for more money.