I have lived in Switzerland for about 5 years now and like the Swiss model.
It is "universal" in the sense that it is compulsory for everyone in the country who is here for more than 3 months. However it is not a single payer plan and is not connected to employment, which makes it portable. Individuals pay for it and do so all of their lives. If you cannot pay the whole premium, your canton (=state) will assist you based on your income. But you own the policy/contract.
There are no pre-existing conditions exclusions and your premiums cannot go up due to your own medical experience -- they are tied to your age group.
My premiums have gone up 1 or 2% each year at most. One year they did not go up at all. It was a shock.
For the basic insurance plan, which is compulsory, the government (or a governament commission, not sure) determines what illnesses are covered and publishes a drug formulary; but it is very comprehensive. It's like the US Blue Cross/Blue Shield used to be. There is no hassle with getting health services (you can go to a general practitioner or directly to a specialist). You show your insurance card and they bill the insurer.
The basic plan is reasonably priced and includes medications and even spa treatments if these are prescribed by a doctor for physical ailments or stress/burnout. Also if you are physically unable to care for yourself or your home due to an illness, you can receive home help until you are better. Some alternative medicines are covered as is acupuncture, for example. So you get doctor visits, lab stuff, medications/equipment, and hospitalization.
What you do not get is a private room in a hospital (only semi-private) or the ability to go outside your canton for treatment. If you want that, you buy a supplemental policy, which about 20-30% of Swiss residents do. It allows for some other benefits as well. Most people are okay with the basic plan. You can never be dumped by your insurer and you can change once a year to another if you would like. The medical staff are well trained and often speak very good English. My wife had a small procedure at our local hospital and was kept in hospital for most of a week (!) to be sure she was okay, and then we had help with house stuff for two weeks following.
There are about 60 nonprofit companies which offer insurance plans, competing on some aspects of price and service.
So in summary, I like that it is not connected to my j*b, making it portable. It is compulsory, so the healthy youngsters are in the pool as well. It covers things like medications and is generally form-free and has the bonus of no hassles/gamesmanship. The companies pay the bills and we are almost never on the 'phone with them as we constantly were when we lived in the US.
One small worry. Switzerland is a true direct democracy. This means citizens can change laws based on majority vote. There is a nationwide referendum this month to switch out the current system with a single-payer government system supported by taxes. I cannot believe this will be better for us; but I don't have a vote here.
BB