The Healing of America: A Global Quest for Better, Cheaper, and Fairer Health Care
It goes into comparing health systems around the world and understanding the history of why they went into effect.
There is a cheeky answer to your question: we have _all_ the main systems that are used in Europe and other places in the world.
There are 4 main systems
1. Beveridge (public health care providers and insurance rolled into one, like the NHS in UK): The VA and healthcare systems used for native americans use this system
2. National health insurance (private healthcare providers and public insurance funded by the government, like Canada's system): Medicare was copied from the Canadian system (even the name!).
3. Bismarck Model: (private healthcare providers and mostly private insurance, along with an individual mandate and heavy regulation of insurance companies: this is used in Germany and Japan). Obamacare was an incomplete attempt to move more towards this model.
4 Out of pocket model: (fully private: a non-system used by most poor countries in the world). This is what the uninsured fall back on.
A less cheeky answer involves looking at the common factor in the rise of systems 1, 2 and 3 in countries around the world. The fundamental political driving force behind this was a moral and ethical decision that healthcare is a human right that the government should provide. When Clinton attempted healthcare reform in 1994 he couched the politics of it in economic terms saying that we need to reduce costs, and it failed. Obamacare only began to make some headway once the politics and debate around it started focusing more on the basic moral and ethical question of whether our society should provide universal access to healthcare.
So it's this weird situation where maybe some people want it for economic reasons (our system is by far the worst in terms of costs per outcome), but politically the best thing is to make this a fundamental moral question of healthcare as a human right. Most constitutions written in the second half of the century include some kind of reference to healthcare as a human right.