Because, of course, they are not totally independent. Medicare is a federal thing. And people would still have to pay into that as well as what the state decides to do.
If you really want to do this and make it work, you need to be in total control and then it can be actually affordable. All Medicare does is pay whatever fees doctors demand. How it works in countries where this is actually done is that with the government being an almost monopoly health care provider, it can say what it will pay and that brings the price down.
For example, I'm British and our NHS works on the basis that doctors get paid what the government says. They can work privately if they want but then they won't get many patients who choose to pay for it. The NHS quite rightly pays them well, just not enough to make them millionaires. As for medication, the NHS is almost the only buyer so it can get away with saying "this is what we will pay" and get a huge bulk discount. And we can do this because we aren't federal - there's just one government.
And no way will it pay for what you don't actually NEED. It will do cosmetic surgery if not having it done affects your mental health, but if you just want a boob job, forget it - you go to a surgeon outside the NHS and you pay full whack.
This is of course socialism in its purest form. And we're not particularly socialist in terms of the usual definition that "the government should control the commanding heights of the economy". But health care is VERY expensive, so this seemed to us the best way to do it. All political arguments in the UK about health care end up being about what's the best way to run the NHS, certainly not about whether we should have it at all.
I love it. I recently had to spend a few days in hospital and it didn't cost me a bean. Another little tarradiddle is to do with the food - of course they need to feed you, and good food helps recovery. NHS food used to be a joke, but one change that has been made recently is that hospitals can contract out to outside caterers. My local hospital uses Apetito and they are fantastic. What we got, in effect, is "Wiltshire Farm Foods" ready made meals that just need to be microwaved. These are publicly sold as well, advertised to old people who don't like to cook or can't cook. My mother lives in a retirement village and I often see Apetito vans there delivering "meals on wheels" - a hot dinner delivered a few days a week by the local council social services. She has had some bad experiences of NHS food as it used to be but I was able to say it wasn't like that for me, and I could show her some examples of what I had on the Wiltshire Farm Foods web site.
As for college, that already exists as others have said.