Australia has had universal health care for over 40 years and it is doing well.. it has its' moments, just like any system. We can pay for extra cover, which is kind of a buffer for what our "medicare" provides. The most notable difference is that our Universal Healthcare has waiting lists for non emergency stuff.
Price wise, we pay a calculated amount for medical, in our taxes. We then can pay extra on a regular basis to a private health cover company - which is calculated on marital status, age etc - tbh it is extremely low compared to the US - but then not all US people pay for their insurance (?)
There are a few things that need fixing - the price of our "buffer" known as Private Health Cover is gradually increasing and people, obviously do not like that. It is also all over the place on what it covers and how much etc. With our universal healthcare, Dental, physio, podiatry and a few other things are not covered - except for certain groups/situations e.g. pensioners, but, as an example, if your podiatrist says you need an operation on your foot, that is covered but a general visit/in house consultation is not
There are a few other things that need tweaking but I guess the biggest thing - in my opinion - is the waiting lists in public hospitals